Cohn, P. M. (Paul Moritz)
Overview
Works:  59 works in 623 publications in 5 languages and 9,304 library holdings 

Roles:  Author, Editor, Collector, Author of introduction, Translator 
Classifications:  QA251.5, 512 
Publication Timeline
.
Most widely held works by
P. M Cohn
Algebra by
P. M Cohn(
Book
)
109 editions published between 1974 and 1996 in 3 languages and held by 1,054 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
109 editions published between 1974 and 1996 in 3 languages and held by 1,054 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
Universal algebra by
P. M Cohn(
Book
)
51 editions published between 1965 and 2002 in 3 languages and held by 948 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
51 editions published between 1965 and 2002 in 3 languages and held by 948 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
)
36 editions published between 1971 and 1985 in 3 languages and held by 768 WorldCat member libraries worldwide
36 editions published between 1971 and 1985 in 3 languages and held by 768 WorldCat member libraries worldwide
Lie groups by
Daniel Bump(
Book
)
51 editions published between 1957 and 2009 in 3 languages and held by 678 WorldCat member libraries worldwide
"This book is intended for a one year graduate course on Lie groups and Lie algebras. The author proceeds beyond the representation theory of compact Lie groups (which is the basis of many texts) and provides a carefully chosen range of material to give the student the bigger picture. For compact Lie groups, the PeterWeyl theorem, conjugacy of maximal tori (two proofs), Weyl character formula and more are covered. The book continues with the study of complex analytic groups, then general noncompact Lie groups, including the Coxeter presentation of the Weyl group, the Iwasawa and Bruhat decompositions, Cartan decomposition, symmetric spaces, Cayley transforms, relative root systems, Satake diagrams, extended Dynkin diagrams and a survey of the ways Lie groups may be embedded in one another. The book culminates in a "topics" section giving depth to the student's understanding of representation theory, taking the FrobeniusSchur duality between the representation theory of the symmetric group and the unitary groups as a unifying theme, with many applications in diverse areas such as random matrix theory, minors of Toeplitz matrices, symmetric algebra decompositions, Gelfand pairs, Hecke algebras, representations of finite general linear groups and the cohomology of Grassmannians and flag varieties
51 editions published between 1957 and 2009 in 3 languages and held by 678 WorldCat member libraries worldwide
"This book is intended for a one year graduate course on Lie groups and Lie algebras. The author proceeds beyond the representation theory of compact Lie groups (which is the basis of many texts) and provides a carefully chosen range of material to give the student the bigger picture. For compact Lie groups, the PeterWeyl theorem, conjugacy of maximal tori (two proofs), Weyl character formula and more are covered. The book continues with the study of complex analytic groups, then general noncompact Lie groups, including the Coxeter presentation of the Weyl group, the Iwasawa and Bruhat decompositions, Cartan decomposition, symmetric spaces, Cayley transforms, relative root systems, Satake diagrams, extended Dynkin diagrams and a survey of the ways Lie groups may be embedded in one another. The book culminates in a "topics" section giving depth to the student's understanding of representation theory, taking the FrobeniusSchur duality between the representation theory of the symmetric group and the unitary groups as a unifying theme, with many applications in diverse areas such as random matrix theory, minors of Toeplitz matrices, symmetric algebra decompositions, Gelfand pairs, Hecke algebras, representations of finite general linear groups and the cohomology of Grassmannians and flag varieties
Introduction to ring theory by
P. M Cohn(
Book
)
23 editions published between 2000 and 2004 in English and Undetermined and held by 547 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
23 editions published between 2000 and 2004 in English and Undetermined and held by 547 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
Algebraic numbers and algebraic functions by
P. M Cohn(
Book
)
21 editions published between 1969 and 1991 in 3 languages and held by 535 WorldCat member libraries worldwide
21 editions published between 1969 and 1991 in 3 languages and held by 535 WorldCat member libraries worldwide
Skew field constructions by
P. M Cohn(
Book
)
20 editions published between 1973 and 1977 in English and Undetermined and held by 459 WorldCat member libraries worldwide
20 editions published between 1973 and 1977 in English and Undetermined and held by 459 WorldCat member libraries worldwide
Skew fields : theory of general division rings by
P. M Cohn(
Book
)
21 editions published between 1995 and 2008 in English and Italian and held by 411 WorldCat member libraries worldwide
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. The treatment of equations over skew fields has been simplified and extended by the use of matrix methods, and the beginnings of noncommutative algebraic geometry are presented, with a precise account of the problems that need to be overcome for a satisfactory theory. A separate chapter describes valuations and orderings on skew fields, with a construction applicable to free fields. Numerous exercises test the reader's understanding, presenting further aspects and open problems in concise form, and notes and comments at the ends of chapters provide historical background
21 editions published between 1995 and 2008 in English and Italian and held by 411 WorldCat member libraries worldwide
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. The treatment of equations over skew fields has been simplified and extended by the use of matrix methods, and the beginnings of noncommutative algebraic geometry are presented, with a precise account of the problems that need to be overcome for a satisfactory theory. A separate chapter describes valuations and orderings on skew fields, with a construction applicable to free fields. Numerous exercises test the reader's understanding, presenting further aspects and open problems in concise form, and notes and comments at the ends of chapters provide historical background
Elements of linear algebra by
P. M Cohn(
Book
)
14 editions published between 1994 and 1999 in English and held by 347 WorldCat member libraries worldwide
14 editions published between 1994 and 1999 in English and held by 347 WorldCat member libraries worldwide
Solid geometry by
P. M Cohn(
Book
)
22 editions published between 1961 and 1968 in English and held by 312 WorldCat member libraries worldwide
22 editions published between 1961 and 1968 in English and held by 312 WorldCat member libraries worldwide
Basic algebra : groups, rings, and fields by
P. M Cohn(
Book
)
20 editions published between 2002 and 2015 in English and Chinese and held by 266 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
20 editions published between 2002 and 2015 in English and Chinese and held by 266 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
Further algebra and applications by
P. M Cohn(
Book
)
19 editions published between 2003 and 2013 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
19 editions published between 2003 and 2013 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 198 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 198 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
)
22 editions published between 1965 and 1976 in English and Undetermined and held by 151 WorldCat member libraries worldwide
22 editions published between 1965 and 1976 in English and Undetermined and held by 151 WorldCat member libraries worldwide
Free rings by
P. M Cohn(
Book
)
6 editions published between 1960 and 1962 in English and Undetermined and held by 50 WorldCat member libraries worldwide
6 editions published between 1960 and 1962 in English and Undetermined and held by 50 WorldCat member libraries worldwide
On the structure of the GL2 of a ring by
P. M Cohn(
Book
)
12 editions published in 1966 in English and held by 45 WorldCat member libraries worldwide
12 editions published in 1966 in English and held by 45 WorldCat member libraries worldwide
Lectures on general algebra by
A. G Kurosh(
Book
)
3 editions published in 1965 in English and held by 28 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 28 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
 Yale University Department of Mathematics
 Howie, James
 Tulane university (La NouvelleOrléans, La.). Organizer of meeting
 Manin, Ju I.
 Lidl, Rudolf Author
 Niederreiter, Harald
 Springer, Tonny Albert (19262011)
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) Field theory (Physics) Geometry Geometry, Solid Group theory Ideals (Algebra) Lie algebras Lie groups Mathematics Matrices Modules (Algebra) Rings Rings (Algebra) Topological groups Topology
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 mathématicien britannique
Paul Moritz Cohn
Кон, П..
Пол Кон английский алгебраист
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