Cohn, P. M. (Paul Moritz)
Overview
Works:  80 works in 674 publications in 7 languages and 9,513 library holdings 

Roles:  Author, Editor, Collector, Author of introduction, Translator 
Classifications:  QA251.5, 512 
Publication Timeline
.
Most widely held works by
P. M Cohn
Universal algebra by
P. M Cohn(
Book
)
57 editions published between 1965 and 2002 in 4 languages and held by 965 WorldCat member libraries worldwide
The present book was conceived as an introduction for the user of universal algebra, rather than a handbook for the specialist, but when the first edition appeared in 1965, there were practically no other books entir~ly devoted to the subject, whether introductory or specialized. Today the specialist in the field is well provided for, but there is still a demand for an introduction to the subject to suit the user, and this seemed to justify a reissue of the book. Naturally some changes have had to be made; in particular, I have corrected all errors that have been brought to my notice. Besides errors, some obscurities in the text have been removed and the references brought up to date. I should like to express my thanks to a number of correspondents for their help, in particular C.G. d'Ambly, W. Felscher, P. Goralcik, P.J. Higgins, H.J. Hoehnke, J.R. Isbell, A.H. Kruse, E.J. Peake, D. Suter, J.S. Wilson. But lowe a special debt to G.M. Bergman, who has provided me with extensive comments. particularly on Chapter VII and the supplementary chapters. I have also con sulted reviews of the first edition, as well as the Italian and Russian translations
57 editions published between 1965 and 2002 in 4 languages and held by 965 WorldCat member libraries worldwide
The present book was conceived as an introduction for the user of universal algebra, rather than a handbook for the specialist, but when the first edition appeared in 1965, there were practically no other books entir~ly devoted to the subject, whether introductory or specialized. Today the specialist in the field is well provided for, but there is still a demand for an introduction to the subject to suit the user, and this seemed to justify a reissue of the book. Naturally some changes have had to be made; in particular, I have corrected all errors that have been brought to my notice. Besides errors, some obscurities in the text have been removed and the references brought up to date. I should like to express my thanks to a number of correspondents for their help, in particular C.G. d'Ambly, W. Felscher, P. Goralcik, P.J. Higgins, H.J. Hoehnke, J.R. Isbell, A.H. Kruse, E.J. Peake, D. Suter, J.S. Wilson. But lowe a special debt to G.M. Bergman, who has provided me with extensive comments. particularly on Chapter VII and the supplementary chapters. I have also con sulted reviews of the first edition, as well as the Italian and Russian translations
Free rings and their relations by
P. M Cohn(
Book
)
39 editions published between 1971 and 1985 in 3 languages and held by 761 WorldCat member libraries worldwide
39 editions published between 1971 and 1985 in 3 languages and held by 761 WorldCat member libraries worldwide
Algebra by
P. M Cohn(
Book
)
58 editions published between 1974 and 1995 in 3 languages and held by 744 WorldCat member libraries worldwide
58 editions published between 1974 and 1995 in 3 languages and held by 744 WorldCat member libraries worldwide
Lie groups by
P. M Cohn(
Book
)
50 editions published between 1957 and 2009 in 3 languages and held by 671 WorldCat member libraries worldwide
50 editions published between 1957 and 2009 in 3 languages and held by 671 WorldCat member libraries worldwide
Introduction to ring theory by
P. M Cohn(
Book
)
26 editions published between 2000 and 2004 in English and held by 551 WorldCat member libraries worldwide
"Most parts of algebra have undergone great changes and advances this century, perhaps none more so than ring theory. In this volume, Paul Cohn provides a clear and structured introduction to the subject." "After a chapter on the definition of rings and modules there are brief accounts of Artinian rings, commutative Noetherian rings and ring constructions, such as the direct product, tensor product and rings of fractions, followed by a description of free rings. The reader is assumed to have a basic understanding of set theory, group theory and vector spaces. Over two hundred carefully selected exercises are included, most with outline solutions."Jacket
26 editions published between 2000 and 2004 in English and held by 551 WorldCat member libraries worldwide
"Most parts of algebra have undergone great changes and advances this century, perhaps none more so than ring theory. In this volume, Paul Cohn provides a clear and structured introduction to the subject." "After a chapter on the definition of rings and modules there are brief accounts of Artinian rings, commutative Noetherian rings and ring constructions, such as the direct product, tensor product and rings of fractions, followed by a description of free rings. The reader is assumed to have a basic understanding of set theory, group theory and vector spaces. Over two hundred carefully selected exercises are included, most with outline solutions."Jacket
Skew field constructions by
P. M Cohn(
Book
)
22 editions published between 1973 and 1977 in English and Undetermined and held by 460 WorldCat member libraries worldwide
22 editions published between 1973 and 1977 in English and Undetermined and held by 460 WorldCat member libraries worldwide
Skew fields : theory of general division rings by
P. M Cohn(
Book
)
25 editions published between 1995 and 2008 in 3 languages and held by 422 WorldCat member libraries worldwide
Noncommutative fields (also called skew fields or division rings) have not been studied as thoroughly as their commutative counterparts and most accounts have hitherto been confined to division algebras, that is skew fields finitedimensional over their centre. Based on the author's LMS lecture note volume Skew Field Constructions, the present work offers a comprehensive account of skew fields. The axiomatic foundation and a precise description of the embedding problem are followed by an account of algebraic and topological construction methods, in particular, the author's general embedding theory is presented with full proofs, leading to the construction of skew fields. The powerful coproduct theorems of G.M. Bergman are proved here as well as the properties of the matrix reduction functor, a useful but littleknown construction providing a source of examples and counterexamples
25 editions published between 1995 and 2008 in 3 languages and held by 422 WorldCat member libraries worldwide
Noncommutative fields (also called skew fields or division rings) have not been studied as thoroughly as their commutative counterparts and most accounts have hitherto been confined to division algebras, that is skew fields finitedimensional over their centre. Based on the author's LMS lecture note volume Skew Field Constructions, the present work offers a comprehensive account of skew fields. The axiomatic foundation and a precise description of the embedding problem are followed by an account of algebraic and topological construction methods, in particular, the author's general embedding theory is presented with full proofs, leading to the construction of skew fields. The powerful coproduct theorems of G.M. Bergman are proved here as well as the properties of the matrix reduction functor, a useful but littleknown construction providing a source of examples and counterexamples
Linear equations by
P. M Cohn(
Book
)
41 editions published between 1958 and 1980 in 3 languages and held by 403 WorldCat member libraries worldwide
LINEAR equations play an important part, not only in mathe matics itself, but also in many fields in which mathematics is used. Whether we deal with elastic deformations or electrical networks, the flutter of aeroplane wings or the estimation of errors by the method of least squares, at some stage in the cal culation we encounter a system of linear equations. In each case the problem of solving the equations is the same, and it is with the mathematical treatment of this question that this book is concerned. By meeting the problem in its pure state the reader will gain an insight which it is hoped will help him when he comes to apply it to his field of work. The actual pro cess of setting up the equations and of interpreting the solution is one which more properly belongs to that field, and in any case is a problem of a different nature altogether. So we need not concern ourselves with it here and are able to concentrate on the mathematical aspect of the situation. The most important tools for handling linear equations are vectors and matrices, and their basic properties are developed in separate chapters. The method by which the nature of the solution is described is one which leads immediately to a solu tion in practical cases, and it is a method frequently adopted when solving problems by mechanical or electronic computers
41 editions published between 1958 and 1980 in 3 languages and held by 403 WorldCat member libraries worldwide
LINEAR equations play an important part, not only in mathe matics itself, but also in many fields in which mathematics is used. Whether we deal with elastic deformations or electrical networks, the flutter of aeroplane wings or the estimation of errors by the method of least squares, at some stage in the cal culation we encounter a system of linear equations. In each case the problem of solving the equations is the same, and it is with the mathematical treatment of this question that this book is concerned. By meeting the problem in its pure state the reader will gain an insight which it is hoped will help him when he comes to apply it to his field of work. The actual pro cess of setting up the equations and of interpreting the solution is one which more properly belongs to that field, and in any case is a problem of a different nature altogether. So we need not concern ourselves with it here and are able to concentrate on the mathematical aspect of the situation. The most important tools for handling linear equations are vectors and matrices, and their basic properties are developed in separate chapters. The method by which the nature of the solution is described is one which leads immediately to a solu tion in practical cases, and it is a method frequently adopted when solving problems by mechanical or electronic computers
Elements of linear algebra by
P. M Cohn(
Book
)
23 editions published between 1994 and 2017 in English and held by 341 WorldCat member libraries worldwide
"This volume presents a thorough discussion of systems of linear equations and their solutions. Vectors and matrices are introduced as required and an account of determinants is given. Great emphasis has been placed on keeping the presentation as simple as possible, with many illustrative examples. While all mathematical assertions are proved, the student is led to view the mathematical content intuitively, as an aid to understanding.The text treats the coordinate geometry of lines, planes and quadrics, provides a natural application for linear algebra and at the same time furnished a geometrical interpretation to illustrate the algebraic concepts."Provided by publisher
23 editions published between 1994 and 2017 in English and held by 341 WorldCat member libraries worldwide
"This volume presents a thorough discussion of systems of linear equations and their solutions. Vectors and matrices are introduced as required and an account of determinants is given. Great emphasis has been placed on keeping the presentation as simple as possible, with many illustrative examples. While all mathematical assertions are proved, the student is led to view the mathematical content intuitively, as an aid to understanding.The text treats the coordinate geometry of lines, planes and quadrics, provides a natural application for linear algebra and at the same time furnished a geometrical interpretation to illustrate the algebraic concepts."Provided by publisher
Solid geometry by
P. M Cohn(
Book
)
24 editions published between 1961 and 1968 in English and held by 310 WorldCat member libraries worldwide
24 editions published between 1961 and 1968 in English and held by 310 WorldCat member libraries worldwide
Algebraic numbers and algebraic functions by
P. M Cohn(
Book
)
13 editions published between 1991 and 2017 in English and held by 309 WorldCat member libraries worldwide
"This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for both using E Artin's legant approach, via valuations. Number Theory is pursued as far as the unit theorem and the finiteness of the class number. In function theory the aim is the AbelJacobi theorem describing the devisor class group, with occasional geometrical asides to help understanding. Assuming only an undergraduate course in algebra, plus a little acquaintance with topology and complex function theory, the book serves as an introduction to more technical works in algebraic number theory, function theory or algebraic geometry by an exposition of the central themes in the subject."Provided by publisher
13 editions published between 1991 and 2017 in English and held by 309 WorldCat member libraries worldwide
"This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for both using E Artin's legant approach, via valuations. Number Theory is pursued as far as the unit theorem and the finiteness of the class number. In function theory the aim is the AbelJacobi theorem describing the devisor class group, with occasional geometrical asides to help understanding. Assuming only an undergraduate course in algebra, plus a little acquaintance with topology and complex function theory, the book serves as an introduction to more technical works in algebraic number theory, function theory or algebraic geometry by an exposition of the central themes in the subject."Provided by publisher
Basic algebra : groups, rings, and fields by
P. M Cohn(
Book
)
24 editions published between 2002 and 2015 in English and Chinese and held by 278 WorldCat member libraries worldwide
Basic Algebra is the first volume of a new and revised edition of P.M. Cohn's classic threevolume text Algebra which is widely regarded as one of the most outstanding introductory algebra textbooks. For this edition, the text has been reworked and updated into two selfcontained, companion volumes, covering advanced topics in algebra for second and thirdyear undergraduate and postgraduate research students. In this first volume, the author covers the important results of algebra; the companion volume, Further Algebra and Applications, brings more advanced topics and focuses on the applications. Readers should have some knowledge of linear algebra and have met groups and fields before, although all the essential facts and definitions are recalled. The coverage is comprehensive and includes topics such as:  Groups  lattices and categories  rings, modules and algebras  fields The author gives a clear account, supported by worked examples, with full proofs. There are numerous exercises with occasional hints, and some historical remarks
24 editions published between 2002 and 2015 in English and Chinese and held by 278 WorldCat member libraries worldwide
Basic Algebra is the first volume of a new and revised edition of P.M. Cohn's classic threevolume text Algebra which is widely regarded as one of the most outstanding introductory algebra textbooks. For this edition, the text has been reworked and updated into two selfcontained, companion volumes, covering advanced topics in algebra for second and thirdyear undergraduate and postgraduate research students. In this first volume, the author covers the important results of algebra; the companion volume, Further Algebra and Applications, brings more advanced topics and focuses on the applications. Readers should have some knowledge of linear algebra and have met groups and fields before, although all the essential facts and definitions are recalled. The coverage is comprehensive and includes topics such as:  Groups  lattices and categories  rings, modules and algebras  fields The author gives a clear account, supported by worked examples, with full proofs. There are numerous exercises with occasional hints, and some historical remarks
Lectures on algebraic numbers and algebraic functions by
P. M Cohn(
Book
)
10 editions published in 1969 in 3 languages and held by 231 WorldCat member libraries worldwide
10 editions published in 1969 in 3 languages and held by 231 WorldCat member libraries worldwide
Further algebra and applications by
P. M Cohn(
Book
)
17 editions published between 2003 and 2004 in English and held by 221 WorldCat member libraries worldwide
"Further Algebra and Applications is the second volume of a new and revised edition of P.M. Cohn's classic threevolume text Algebra which is widely regarded as one of the most outstanding introductory algebra textbooks. For this edition, the text has been reworked and updated into two selfcontained, companion volumes, covering advanced topics in algebra for second and thirdyear undergraduate and postgraduate research students"Jacket
17 editions published between 2003 and 2004 in English and held by 221 WorldCat member libraries worldwide
"Further Algebra and Applications is the second volume of a new and revised edition of P.M. Cohn's classic threevolume text Algebra which is widely regarded as one of the most outstanding introductory algebra textbooks. For this edition, the text has been reworked and updated into two selfcontained, companion volumes, covering advanced topics in algebra for second and thirdyear undergraduate and postgraduate research students"Jacket
Free ideal rings and localization in general rings by
P. M Cohn(
Book
)
13 editions published between 2005 and 2006 in English and held by 199 WorldCat member libraries worldwide
"This book presents the theory of free ideal rings (firs) in detail. Particular emphasis in placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization, which is treated for general rings but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends with a historical note."Jacket
13 editions published between 2005 and 2006 in English and held by 199 WorldCat member libraries worldwide
"This book presents the theory of free ideal rings (firs) in detail. Particular emphasis in placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization, which is treated for general rings but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends with a historical note."Jacket
Classic algebra by
P. M Cohn(
Book
)
16 editions published between 2000 and 2001 in English and held by 152 WorldCat member libraries worldwide
16 editions published between 2000 and 2001 in English and held by 152 WorldCat member libraries worldwide
Morita equivalence and duality by
P. M Cohn(
Book
)
26 editions published between 1965 and 1994 in English and held by 147 WorldCat member libraries worldwide
26 editions published between 1965 and 1994 in English and held by 147 WorldCat member libraries worldwide
Algebra by
P. M Cohn(
Book
)
18 editions published between 1977 and 1995 in English and held by 109 WorldCat member libraries worldwide
18 editions published between 1977 and 1995 in English and held by 109 WorldCat member libraries worldwide
Algebra by
P. M Cohn(
Book
)
21 editions published between 1974 and 1997 in English and Dutch and held by 96 WorldCat member libraries worldwide
21 editions published between 1974 and 1997 in English and Dutch and held by 96 WorldCat member libraries worldwide
Lectures on general algebra by
A. G Kurosh(
Book
)
3 editions published in 1965 in English and held by 27 WorldCat member libraries worldwide
Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University
3 editions published in 1965 in English and held by 27 WorldCat member libraries worldwide
Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Kurosh, A. G. (Aleksandr Gennadievich) Author Editor
 Swinfen, Ann Translator
 Bourbaki, Nicolas Author
 Manin, Ju I.
 Lidl, Rudolf Author
 Yale University Department of Mathematics
 Tulane university (La NouvelleOrléans, La.) Organizer of meeting
 Niederreiter, Harald Other
 Springer, Tonny Albert (19262011)
 Howie, James Translator
Useful Links
Associated Subjects
Algebra Algebra, Abstract Algebra, Universal Algebraic fields Algebraic functions Algebraic number theory Algebraic topology Algebras, Linear Associative algebras Associative rings Categories (Mathematics) Division rings Duality theory (Mathematics) Equations Equations, Simultaneous Field theory (Physics) Geometry Geometry, Solid Group theory Ideals (Algebra) Lie groups Mathematics Matrices Modules (Algebra) Rings Rings (Algebra) Topology Vector analysis
Alternative Names
Cohn, P. M.
Cohn, P. M. 19242006
Cohn, Paul 19242006
Cohn, Paul M.
Cohn, Paul Moritz
Cohn, Paul Moritz 19242006
Kon, P.
Kon, P. 19242006
Kon, P. M.
Kon, P. M. (Paul Moritz)
Paul Cohn britischer Mathematiker
Paul Cohn britisk matematikar
Paul Cohn britisk matematiker
Paul Cohn Brits wiskundige (19242006)
Paul Cohn brittisk matematiker
Paul Cohn German mathematician
Paul Cohn matemático alemán
Paul Cohn mathématicien britannique
Paul Moritz Cohn
Кон, П..
Пол Кон английский алгебраист
פול כהן
פול כהן מתמטיקאי גרמני
پل کوهن ریاضیدان بریتانیایی
ポール・コーン
保羅·孔恩
鲍尔·科恩
Languages
Covers