Cohn, P. M. (Paul Moritz)
Overview
Works:  121 works in 782 publications in 7 languages and 11,091 library holdings 

Roles:  Author, Editor, Author of introduction, Translator, Collector, htt 
Classifications:  QA251.5, 512.4 
Publication Timeline
.
Most widely held works by
P. M Cohn
Skew fields : theory of general division rings by
P. M Cohn(
)
23 editions published between 1995 and 2008 in English and Italian and held by 1,657 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
23 editions published between 1995 and 2008 in English and Italian and held by 1,657 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
Universal algebra by
P. M Cohn(
Book
)
38 editions published between 1965 and 1981 in 4 languages and held by 922 WorldCat member libraries worldwide
38 editions published between 1965 and 1981 in 4 languages and held by 922 WorldCat member libraries worldwide
Free ideal rings and localization in general rings by
P. M Cohn(
)
18 editions published between 2005 and 2006 in English and held by 891 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
18 editions published between 2005 and 2006 in English and held by 891 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
Free rings and their relations by
P. M Cohn(
Book
)
30 editions published between 1971 and 1985 in 3 languages and held by 746 WorldCat member libraries worldwide
30 editions published between 1971 and 1985 in 3 languages and held by 746 WorldCat member libraries worldwide
Lie groups by
P. M Cohn(
Book
)
57 editions published between 1957 and 2009 in 3 languages and held by 703 WorldCat member libraries worldwide
57 editions published between 1957 and 2009 in 3 languages and held by 703 WorldCat member libraries worldwide
Introduction to ring theory by
P. M Cohn(
Book
)
29 editions published between 2000 and 2004 in English and German and held by 656 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
29 editions published between 2000 and 2004 in English and German and held by 656 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
Linear equations by
P. M Cohn(
Book
)
45 editions published between 1958 and 1980 in 3 languages and held by 462 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
45 editions published between 1958 and 1980 in 3 languages and held by 462 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
Skew field constructions by
P. M Cohn(
Book
)
15 editions published in 1977 in English and Undetermined and held by 428 WorldCat member libraries worldwide
"These notes describe methods of constructing skew fields, in particular the coproduct coconstruction discovered by the author, and trace out some of the consequences using the powerful coproduct theorems of G.M. Bergman, which are proved here." publisher
15 editions published in 1977 in English and Undetermined and held by 428 WorldCat member libraries worldwide
"These notes describe methods of constructing skew fields, in particular the coproduct coconstruction discovered by the author, and trace out some of the consequences using the powerful coproduct theorems of G.M. Bergman, which are proved here." publisher
Elements of linear algebra by
P. M Cohn(
Book
)
26 editions published between 1994 and 2017 in English and held by 406 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
26 editions published between 1994 and 2017 in English and held by 406 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
Algebraic numbers and algebraic functions by
P. M Cohn(
Book
)
19 editions published between 1991 and 2018 in English and Undetermined and held by 399 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
19 editions published between 1991 and 2018 in English and Undetermined and held by 399 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
Basic algebra : groups, rings, and fields by
P. M Cohn(
Book
)
29 editions published between 2002 and 2015 in 3 languages and held by 397 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
29 editions published between 2002 and 2015 in 3 languages and held by 397 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 in general algebra by
A. G Kurosh(
Book
)
3 editions published in 1965 in English and held by 332 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 332 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
Further algebra and applications by
P. M Cohn(
Book
)
20 editions published between 2003 and 2004 in English and German and held by 330 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
20 editions published between 2003 and 2004 in English and German and held by 330 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
Solid geometry by
P. M Cohn(
Book
)
26 editions published between 1961 and 1968 in English and Undetermined and held by 301 WorldCat member libraries worldwide
26 editions published between 1961 and 1968 in English and Undetermined and held by 301 WorldCat member libraries worldwide
Lectures on algebraic numbers and algebraic functions by
P. M Cohn(
Book
)
11 editions published in 1969 in 3 languages and held by 246 WorldCat member libraries worldwide
11 editions published in 1969 in 3 languages and held by 246 WorldCat member libraries worldwide
Algebra by
P. M Cohn(
Book
)
3 editions published in 1995 in English and held by 228 WorldCat member libraries worldwide
3 editions published in 1995 in English and held by 228 WorldCat member libraries worldwide
Algebra by
P. M Cohn(
Book
)
65 editions published between 1974 and 1997 in 3 languages and held by 176 WorldCat member libraries worldwide
65 editions published between 1974 and 1997 in 3 languages and held by 176 WorldCat member libraries worldwide
Classic algebra by
P. M Cohn(
Book
)
19 editions published between 2000 and 2001 in English and held by 164 WorldCat member libraries worldwide
19 editions published between 2000 and 2001 in English and held by 164 WorldCat member libraries worldwide
Morita equivalence and duality by
P. M Cohn(
Book
)
28 editions published between 1965 and 1994 in English and Undetermined and held by 155 WorldCat member libraries worldwide
28 editions published between 1965 and 1994 in English and Undetermined and held by 155 WorldCat member libraries worldwide
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Audience Level
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Kids  General  Special 
Related Identities
 Kurosh, A. G. (Aleksandr Gennadievich) Author Editor
 Swinfen, Ann Translator
 Bourbaki, Nicolas Author
 Lidl, Rudolf Author
 Niederreiter, Harald 1944 Other
 Howie, James Translator
 Robinson, Gilbert de B. (Gilbert de Beauregard) 19061992 Author of introduction
 James, G. D. (Gordon Douglas) 1945 Author
 Kerber, Adalbert Other
 Tulane university (La NouvelleOrléans, La.). Organizer of meeting
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Associated Subjects
Algebra Algebra, Abstract Algebra, Universal Algebraic fields Algebraic functions Algebraic number theory Algebraic topology Algebras, Linear Associative algebras Associative rings Categories (Mathematics) Differential equations, Linear Division rings Duality theory (Mathematics) Engineering mathematics Equations Equations, Simultaneous Field theory (Physics) Flood forecastingMathematical models Geometry Geometry, Solid Group theory Ideals (Algebra) Lie groups Mathematics Matrices Modules (Algebra) Number theory Ordered algebraic structures Rings Rings (Algebra) Topology Vector analysis
Covers
Alternative Names
Cohn, P. M.
Cohn, P. M. 19242006
Cohn, Paul 19242006
Cohn, Paul M.
Cohn, Paul M. (Paul Moritz)
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 matemàtic alemany
Paul Cohn matemático alemán
Paul Cohn matematico tedesco
Paul Cohn matemáticu alemán
Paul Cohn matematikan gjerman
Paul Cohn mathématicien britannique
Paul Cohn professor académico alemão
Paul Moritz Cohn
Кон, П..
Кон, П. (Паул)
Пол Кон английский алгебраист
פול כהן
פול כהן מתמטיקאי גרמני
پاول كوهن
پل کوهن ریاضیدان بریتانیایی
ポール・コーン
保羅·孔恩
保羅·孔恩 英国数学教授
鲍尔·科恩
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