# Lectures on Rings and Modules

## Lambek, Joachim

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This book is an introduction to the theory of associative rings and their modules, designed primarily for graduate students. The standard topics on the structure of rings are covered, with a particular emphasis on the concept of the complete ring of quotients. A survey of the fundamental concepts of algebras in the first chapter helps to make the treatment self-contained. The topics covered include selected results on Boolean and other commutative rings, the classical structure theory of associative rings, injective modules, and rings of quotients. The final chapter provides an introduction to homological algebra. Besides three appendices on further results, there is a six-page section of historical comments. Table of Contents: Fundamental Concepts of Algebra: 1.1 Rings and related algebraic systems; 1.2 Subrings, homomorphisms, ideals; 1.3 Modules, direct products, and direct sums; 1.4 Classical isomorphism theorems. Selected Topics on Commutative Rings: 2.1 Prime ideals in commutative rings; 2.2 Prime ideals in special commutative rings; 2.3 The complete ring of quotients of a commutative ring; 2.4 Rings of quotients of commutative semiprime rings; 2.5 Prime ideal spaces. Classical Theory of Associative Rings: 3.1 Primitive rings; 3.2 Radicals; 3.3 Completely reducible modules; 3.4 Completely reducible rings; 3.5 Artinian and Noetherian rings; 3.6 On lifting idempotents; 3.7 Local and semiperfect rings. Injectivity and Related Concepts: 4.1 Projective modules; 4.2 Injective modules; 4.3 The complete ring of quotients; 4.4 Rings of endomorphisms of injective modules; 4.5 Regular rings of quotients; 4.6 Classical rings of quotients; 4.7 The Faith-Utumi theorem. Introduction to Homological Algebra: 5.1 Tensor products of modules; 5.2 Hom and $\otimes$ as functors; 5.3 Exact sequences; 5.4 Flat modules; 5.5 Torsion and extension products. Appendixes; Comments; Bibliography; Index. Review from Zentralblatt Math: Due to their clarity and intelligible presentation, these lectures on rings and modules are a particularly successful introduction to the surrounding circle of ideas. Review from American Mathematical Monthly: An introduction to associative rings and modules which requires of the reader only the mathematical maturity which one would attain in a first-year graduate algebra [course]...in order to make the contents of the book as accessible as possible, the author develops all the fundamentals he will need. In addition to covering the basic topics...the author covers some topics not so readily available to the nonspecialist...the chapters are written to be as independent as possible...[which will be appreciated by] students making their first acquaintance with the subject...one of the most successful features of the book is that it can be read by graduate students with little or no help from a specialist. (CHEL/283.H)

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## 1.Lectures On Rings And Modules

ISBN 10: 082184900X ISBN 13: 9780821849002
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Descrizione libro Condizione libro: New. Depending on your location, this item may ship from the US or UK. Codice libro della libreria 97808218490020000000

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## 2.Lectures on Rings and Modules (Hardback)

Editore: American Mathematical Society, United States (2010)
ISBN 10: 082184900X ISBN 13: 9780821849002
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Descrizione libro American Mathematical Society, United States, 2010. Hardback. Condizione libro: New. 3rd. 234 x 157 mm. Language: English . Brand New Book. This book is an introduction to the theory of associative rings and their modules, designed primarily for graduate students. The standard topics on the structure of rings are covered, with a particular emphasis on the concept of the complete ring of quotients. A survey of the fundamental concepts of algebras in the first chapter helps to make the treatment self-contained. The topics covered include selected results on Boolean and other commutative rings, the classical structure theory of associative rings, injective modules, and rings of quotients. The final chapter provides an introduction to homological algebra. Besides three appendices on further results, there is a six-page section of historical comments. Table of Contents: Fundamental Concepts of Algebra: 1.1 Rings and related algebraic systems; 1.2 Subrings, homomorphisms, ideals; 1.3 Modules, direct products, and direct sums; 1.4 Classical isomorphism theorems. Selected Topics on Commutative Rings: 2.1 Prime ideals in commutative rings; 2.2 Prime ideals in special commutative rings; 2.3 The complete ring of quotients of a commutative ring; 2.4 Rings of quotients of commutative semiprime rings; 2.5 Prime ideal spaces. Classical Theory of Associative Rings: 3.1 Primitive rings; 3.2 Radicals; 3.3 Completely reducible modules; 3.4 Completely reducible rings; 3.5 Artinian and Noetherian rings; 3.6 On lifting idempotents; 3.7 Local and semiperfect rings. Injectivity and Related Concepts: 4.1 Projective modules; 4.2 Injective modules; 4.3 The complete ring of quotients; 4.4 Rings of endomorphisms of injective modules; 4.5 Regular rings of quotients; 4.6 Classical rings of quotients; 4.7 The Faith-Utumi theorem. Introduction to Homological Algebra: 5.1 Tensor products of modules; 5.2 Hom and $otimes$ as functors; 5.3 Exact sequences; 5.4 Flat modules; 5.5 Torsion and extension products. Appendixes; Comments; Bibliography; Index. Review from Zentralblatt Math: Due to their clarity and intelligible presentation, these lectures on rings and modules are a particularly successful introduction to the surrounding circle of ideas. Review from American Mathematical Monthly: An introduction to associative rings and modules which requires of the reader only the mathematical maturity which one would attain in a first-year graduate algebra [course].in order to make the contents of the book as accessible as possible, the author develops all the fundamentals he will need. In addition to covering the basic topics.the author covers some topics not so readily available to the nonspecialist.the chapters are written to be as independent as possible.[which will be appreciated by] students making their first acquaintance with the subject.one of the most successful features of the book is that it can be read by graduate students with little or no help from a specialist. (CHEL/283.H). Codice libro della libreria AAN9780821849002

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## 3.Lectures on Rings and Modules (Hardback)

Editore: American Mathematical Society, United States (2010)
ISBN 10: 082184900X ISBN 13: 9780821849002
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Descrizione libro American Mathematical Society, United States, 2010. Hardback. Condizione libro: New. 3rd. 234 x 157 mm. Language: English . Brand New Book. This book is an introduction to the theory of associative rings and their modules, designed primarily for graduate students. The standard topics on the structure of rings are covered, with a particular emphasis on the concept of the complete ring of quotients. A survey of the fundamental concepts of algebras in the first chapter helps to make the treatment self-contained. The topics covered include selected results on Boolean and other commutative rings, the classical structure theory of associative rings, injective modules, and rings of quotients. The final chapter provides an introduction to homological algebra. Besides three appendices on further results, there is a six-page section of historical comments. Table of Contents: Fundamental Concepts of Algebra: 1.1 Rings and related algebraic systems; 1.2 Subrings, homomorphisms, ideals; 1.3 Modules, direct products, and direct sums; 1.4 Classical isomorphism theorems. Selected Topics on Commutative Rings: 2.1 Prime ideals in commutative rings; 2.2 Prime ideals in special commutative rings; 2.3 The complete ring of quotients of a commutative ring; 2.4 Rings of quotients of commutative semiprime rings; 2.5 Prime ideal spaces. Classical Theory of Associative Rings: 3.1 Primitive rings; 3.2 Radicals; 3.3 Completely reducible modules; 3.4 Completely reducible rings; 3.5 Artinian and Noetherian rings; 3.6 On lifting idempotents; 3.7 Local and semiperfect rings. Injectivity and Related Concepts: 4.1 Projective modules; 4.2 Injective modules; 4.3 The complete ring of quotients; 4.4 Rings of endomorphisms of injective modules; 4.5 Regular rings of quotients; 4.6 Classical rings of quotients; 4.7 The Faith-Utumi theorem. Introduction to Homological Algebra: 5.1 Tensor products of modules; 5.2 Hom and $otimes$ as functors; 5.3 Exact sequences; 5.4 Flat modules; 5.5 Torsion and extension products. Appendixes; Comments; Bibliography; Index. Review from Zentralblatt Math: Due to their clarity and intelligible presentation, these lectures on rings and modules are a particularly successful introduction to the surrounding circle of ideas. Review from American Mathematical Monthly: An introduction to associative rings and modules which requires of the reader only the mathematical maturity which one would attain in a first-year graduate algebra [course].in order to make the contents of the book as accessible as possible, the author develops all the fundamentals he will need. In addition to covering the basic topics.the author covers some topics not so readily available to the nonspecialist.the chapters are written to be as independent as possible.[which will be appreciated by] students making their first acquaintance with the subject.one of the most successful features of the book is that it can be read by graduate students with little or no help from a specialist. (CHEL/283.H). Codice libro della libreria AAN9780821849002

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## 4.Lectures on Rings and Modules (3rd)

Editore: American Mathematical Society
ISBN 10: 082184900X ISBN 13: 9780821849002
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Descrizione libro American Mathematical Society. Hardback. Condizione libro: new. BRAND NEW, Lectures on Rings and Modules (3rd), Joachim Lambek, This book is an introduction to the theory of associative rings and their modules, designed primarily for graduate students. The standard topics on the structure of rings are covered, with a particular emphasis on the concept of the complete ring of quotients. A survey of the fundamental concepts of algebras in the first chapter helps to make the treatment self-contained. The topics covered include selected results on Boolean and other commutative rings, the classical structure theory of associative rings, injective modules, and rings of quotients. The final chapter provides an introduction to homological algebra. Besides three appendices on further results, there is a six-page section of historical comments. Table of Contents: Fundamental Concepts of Algebra: 1.1 Rings and related algebraic systems; 1.2 Subrings, homomorphisms, ideals; 1.3 Modules, direct products, and direct sums; 1.4 Classical isomorphism theorems. Selected Topics on Commutative Rings: 2.1 Prime ideals in commutative rings; 2.2 Prime ideals in special commutative rings; 2.3 The complete ring of quotients of a commutative ring; 2.4 Rings of quotients of commutative semiprime rings; 2.5 Prime ideal spaces. Classical Theory of Associative Rings: 3.1 Primitive rings; 3.2 Radicals; 3.3 Completely reducible modules; 3.4 Completely reducible rings; 3.5 Artinian and Noetherian rings; 3.6 On lifting idempotents; 3.7 Local and semiperfect rings. Injectivity and Related Concepts: 4.1 Projective modules; 4.2 Injective modules; 4.3 The complete ring of quotients; 4.4 Rings of endomorphisms of injective modules; 4.5 Regular rings of quotients; 4.6 Classical rings of quotients; 4.7 The Faith-Utumi theorem. Introduction to Homological Algebra: 5.1 Tensor products of modules; 5.2 Hom and $\otimes$ as functors; 5.3 Exact sequences; 5.4 Flat modules; 5.5 Torsion and extension products. Appendixes; Comments; Bibliography; Index. Review from Zentralblatt Math: Due to their clarity and intelligible presentation, these lectures on rings and modules are a particularly successful introduction to the surrounding circle of ideas. Review from American Mathematical Monthly: An introduction to associative rings and modules which requires of the reader only the mathematical maturity which one would attain in a first-year graduate algebra [course].in order to make the contents of the book as accessible as possible, the author develops all the fundamentals he will need. In addition to covering the basic topics.the author covers some topics not so readily available to the nonspecialist.the chapters are written to be as independent as possible.[which will be appreciated by] students making their first acquaintance with the subject.one of the most successful features of the book is that it can be read by graduate students with little or no help from a specialist. (CHEL/283.H). Codice libro della libreria B9780821849002

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## 5.Lectures on Rings and Modules

Editore: American Mathematical Society (2010)
ISBN 10: 082184900X ISBN 13: 9780821849002
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Descrizione libro American Mathematical Society, 2010. HRD. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria CE-9780821849002

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## 6.Lectures on Rings and Modules (AMS Chelsea Publishing)

Editore: American Mathematical Society (2009)
ISBN 10: 082184900X ISBN 13: 9780821849002
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Descrizione libro American Mathematical Society, 2009. Hardcover. Condizione libro: New. 3rd. Codice libro della libreria DADAX082184900X

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## 7.Lectures on Rings and Modules (AMS Chelsea Publishing)

Editore: American Mathematical Society (2009)
ISBN 10: 082184900X ISBN 13: 9780821849002
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Descrizione libro American Mathematical Society, 2009. Hardcover. Condizione libro: New. 3rd. Brand new. We distribute directly for the publisher. This book is an introduction to the theory of associative rings and their modules, designed primarily for graduate students. The standard topics on the structure of rings are covered, with a particular emphasis on the concept of the complete ring of quotients.A survey of the fundamental concepts of algebras in the first chapter helps to make the treatment self-contained. The topics covered include selected results on Boolean and other commutative rings, the classical structure theory of associative rings, injective modules, and rings of quotients. The final chapter provides an introduction to homological algebra. Besides three appendices on further results, there is a six-page section of historical comments. Codice libro della libreria 1602160029

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## 8.Lectures on Rings and Modules (AMS Chelsea Publishing)

Editore: American Mathematical Society (2009)
ISBN 10: 082184900X ISBN 13: 9780821849002
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Descrizione libro American Mathematical Society, 2009. Hardcover. Condizione libro: New. book. Codice libro della libreria 082184900X

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## 9.Lectures on Rings and Modules

Editore: American Mathematical Society (2009)
ISBN 10: 082184900X ISBN 13: 9780821849002
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Descrizione libro American Mathematical Society, 2009. Condizione libro: New. Editor(s): Lambek, Joachim. Series: AMS Chelsea Publishing. Num Pages: 185 pages. BIC Classification: PBF. Category: (P) Professional & Vocational. Dimension: 159 x 232 x 16. Weight in Grams: 400. . 2009. 3rd. Hardcover. . . . . . Codice libro della libreria V9780821849002

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## 10.Lectures on Rings and Modules

ISBN 10: 082184900X ISBN 13: 9780821849002
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Descrizione libro Hardback. Condizione libro: New. Not Signed; This book is an introduction to the theory of associative rings and their modules, designed primarily for graduate students. The standard topics on the structure of rings are covered, with a particular emphasis on the concept of the complete ring of quotients. A survey of the fundamental concepts of. book. Codice libro della libreria ria9780821849002_rkm

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