Cohn, P. M. (Paul Moritz)
Overview
Works:  76 works in 659 publications in 7 languages and 9,468 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 970 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 970 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
Algebra by
P. M Cohn(
Book
)
68 editions published between 1974 and 1995 in 3 languages and held by 823 WorldCat member libraries worldwide
Sets and mappings; Integers and rational numbers; Groups; Vector spaces and linear mapping; Linear equations; Rings and fields; Determinants; Quadratic forms; Further group theory; Rings and modules; Normal forms for matrices
68 editions published between 1974 and 1995 in 3 languages and held by 823 WorldCat member libraries worldwide
Sets and mappings; Integers and rational numbers; Groups; Vector spaces and linear mapping; Linear equations; Rings and fields; Determinants; Quadratic forms; Further group theory; Rings and modules; Normal forms for matrices
Free rings and their relations by
P. M Cohn(
Book
)
39 editions published between 1971 and 1985 in 3 languages and held by 767 WorldCat member libraries worldwide
39 editions published between 1971 and 1985 in 3 languages and held by 767 WorldCat member libraries worldwide
Lie groups by
P. M Cohn(
Book
)
50 editions published between 1957 and 2009 in 3 languages and held by 676 WorldCat member libraries worldwide
50 editions published between 1957 and 2009 in 3 languages and held by 676 WorldCat member libraries worldwide
Introduction to ring theory by
P. M Cohn(
Book
)
26 editions published between 2000 and 2004 in English and Undetermined and held by 549 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 Undetermined and held by 549 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
)
21 editions published between 1973 and 1977 in English and Undetermined and held by 462 WorldCat member libraries worldwide
21 editions published between 1973 and 1977 in English and Undetermined and held by 462 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 416 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 finite dimensional 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, is 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 theorem of G. M. Bergman is proved here, as well as the properties of the matrix reduction functor, a useful but littleknown construction providing a source of examples and counterexamples. The construction and basic properties of existentially closed skew fields are given, leading to an example of a model class with an infinite forcing companion which is not axiomatizable
25 editions published between 1995 and 2008 in 3 languages and held by 416 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 finite dimensional 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, is 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 theorem of G. M. Bergman is proved here, as well as the properties of the matrix reduction functor, a useful but littleknown construction providing a source of examples and counterexamples. The construction and basic properties of existentially closed skew fields are given, leading to an example of a model class with an infinite forcing companion which is not axiomatizable
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
)
14 editions published between 1994 and 1999 in English and held by 341 WorldCat member libraries worldwide
14 editions published between 1994 and 1999 in English and held by 341 WorldCat member libraries worldwide
Solid geometry by
P. M Cohn(
Book
)
23 editions published between 1961 and 1968 in English and held by 317 WorldCat member libraries worldwide
23 editions published between 1961 and 1968 in English and held by 317 WorldCat member libraries worldwide
Algebraic numbers and algebraic functions by
P. M Cohn(
Book
)
12 editions published in 1991 in English and held by 307 WorldCat member libraries worldwide
12 editions published in 1991 in English and held by 307 WorldCat member libraries worldwide
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 274 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 274 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
)
9 editions published in 1969 in 3 languages and held by 229 WorldCat member libraries worldwide
9 editions published in 1969 in 3 languages and held by 229 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 220 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. The first volume, "Basic Algebra", covers the important results of algebra; this companion volume focuses on the applications and covers the more advanced parts of topics such as:  groups and algebras  homological algebra  universal algebra  general ring theory  representations of finite groups  coding theory  languages and automata The author gives a clear account, supported by worked examples, with full proofs. There are numerous exercises with occasional hints, and some historical remarks
17 editions published between 2003 and 2004 in English and held by 220 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. The first volume, "Basic Algebra", covers the important results of algebra; this companion volume focuses on the applications and covers the more advanced parts of topics such as:  groups and algebras  homological algebra  universal algebra  general ring theory  representations of finite groups  coding theory  languages and automata The author gives a clear account, supported by worked examples, with full proofs. There are numerous exercises with occasional hints, and some historical remarks
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 197 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 197 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
)
25 editions published between 1965 and 1994 in English and Undetermined and held by 150 WorldCat member libraries worldwide
25 editions published between 1965 and 1994 in English and Undetermined and held by 150 WorldCat member libraries worldwide
Algebra by
P. M Cohn(
Book
)
20 editions published between 1974 and 1997 in English and Dutch and held by 93 WorldCat member libraries worldwide
20 editions published between 1974 and 1997 in English and Dutch and held by 93 WorldCat member libraries worldwide
On the structure of the GL2 of a ring by
P. M Cohn(
Book
)
14 editions published in 1966 in English and held by 51 WorldCat member libraries worldwide
14 editions published in 1966 in English and held by 51 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
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Related Identities
 Kurosh, A. G. (Aleksandr Gennadievich) Author Editor
 Swinfen, Ann Translator
 Bourbaki, Nicolas Author
 Manin, Ju I.
 Yale University Department of Mathematics
 Tulane university (La NouvelleOrléans, La.) Organizer of meeting
 Lidl, Rudolf Author
 Niederreiter, Harald Other
 Springer, Tonny Albert (19262011)
 Howie, James Translator
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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) Division rings Duality theory (Mathematics) Equations Equations, Simultaneous Field theory (Physics) Geometry Geometry, Solid Group theory Ideals (Algebra) Lie algebras 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
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