Hardcover ISBN:  9780821847992 
Product Code:  GSM/100 
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AMS Member Price:  $70.40 
Electronic ISBN:  9781470411640 
Product Code:  GSM/100.E 
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Book DetailsGraduate Studies in MathematicsVolume: 100; 1994; 516 ppMSC: Primary 00; Secondary 12; 13; 16; 20;
This book, based on a firstyear graduate course the author taught at the University of Wisconsin, contains more than enough material for a twosemester graduatelevel abstract algebra course, including groups, rings and modules, fields and Galois theory, an introduction to algebraic number theory, and the rudiments of algebraic geometry. In addition, there are some more specialized topics not usually covered in such a course. These include transfer and character theory of finite groups, modules over artinian rings, modules over Dedekind domains, and transcendental field extensions.
This book could be used for self study as well as for a course text, and so full details of almost all proofs are included, with nothing being relegated to the chapterend problems. There are, however, hundreds of problems, many being far from trivial. The book attempts to capture some of the informality of the classroom, as well as the excitement the author felt when taking the corresponding course as a student.
Originally published by Brooks Cole/Cengage Learning as ISBN: 9780534190026ReadershipGraduate students and research mathematicians interested in algebra.

Table of Contents

Part One. Noncommutative algebra

Chapter 1. Definitions and examples of groups

Chapter 2. Subgroups and cosets

Chapter 3. Homomorphisms

Chapter 4. Group actions

Chapter 5. The Sylow theorems and $p$groups

Chapter 6. Permutation groups

Chapter 7. New groups from old

Chapter 8. Solvable and nilpotent groups

Chapter 9. Transfer

Chapter 10. Operator groups and unique decompositions

Chapter 11. Module theory without rings

Chapter 12. Rings, ideals, and modules

Chapter 13. Simple modules and primitive rings

Chapter 14. Artinian rings and projective modules

Chapter 15. An introduction to character theory

Part Two. Commutative algebra

Chapter 16. Polynomial rings, PIDs, and UFDs

Chapter 17. Field extensions

Chapter 18. Galois theory

Chapter 19. Separability and inseparability

Chapter 20. Cyclotomy and geometric constructions

Chapter 21. Finite fields

Chapter 22. Roots, radicals, and real numbers

Chapter 23. Norms, traces, and discriminants

Chapter 24. Transcendental extensions

Chapter 25. the ArtinSchreier theorem

Chapter 26. Ideal theory

Chapter 27. Noetherian rings

Chapter 28. Integrality

Chapter 29. Dedekind domains

Chapter 30. Algebraic sets and the Nullstellensatz


Additional Material

Reviews

Unlike similar textbooks, this volume steers away from chapterend problems by including full details of all proofs as problems are presented.
SciTech Book News 
This is a book to be warmly welcomed. The presentation throughout is a model of clarity, and the proofs are precise and complete. The careful reader will learn (much) from it, not only mathematics, but also (and more importantly) how to think mathematically.
Mathematical Reviews 
Isaacs' Algebra, A Graduate Course is a pedagogically important book, to be highly recommended to fledgling algebraists—and every one else, for that matter.
MAA Reviews 
Most of these extra topics are not usually covered in firstyear graduate algebra courses, or in introductory textbooks on modern algebra, but here they are woven into the main text in very natural, effective and instructive a manner, thereby offering a wider panorama of abstract algebra to the interested reader. This profound algebra text will prepare any zealous reader for further steps into one or more of the many branches of algebra, algebraic number theory, or algebraic geometry. Also, it will maintain its wellestablished role as one of the excellent standard texts on the subject, as a highly recommendable source for instructors, and as an utmost valuable companion to the various other great textbooks in the field.
Zentralblatt MATH


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 Book Details
 Table of Contents
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 Request Review Copy
 Request Exam/Desk Copy
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This book, based on a firstyear graduate course the author taught at the University of Wisconsin, contains more than enough material for a twosemester graduatelevel abstract algebra course, including groups, rings and modules, fields and Galois theory, an introduction to algebraic number theory, and the rudiments of algebraic geometry. In addition, there are some more specialized topics not usually covered in such a course. These include transfer and character theory of finite groups, modules over artinian rings, modules over Dedekind domains, and transcendental field extensions.
This book could be used for self study as well as for a course text, and so full details of almost all proofs are included, with nothing being relegated to the chapterend problems. There are, however, hundreds of problems, many being far from trivial. The book attempts to capture some of the informality of the classroom, as well as the excitement the author felt when taking the corresponding course as a student.
Originally published by Brooks Cole/Cengage Learning as ISBN: 9780534190026
Graduate students and research mathematicians interested in algebra.

Part One. Noncommutative algebra

Chapter 1. Definitions and examples of groups

Chapter 2. Subgroups and cosets

Chapter 3. Homomorphisms

Chapter 4. Group actions

Chapter 5. The Sylow theorems and $p$groups

Chapter 6. Permutation groups

Chapter 7. New groups from old

Chapter 8. Solvable and nilpotent groups

Chapter 9. Transfer

Chapter 10. Operator groups and unique decompositions

Chapter 11. Module theory without rings

Chapter 12. Rings, ideals, and modules

Chapter 13. Simple modules and primitive rings

Chapter 14. Artinian rings and projective modules

Chapter 15. An introduction to character theory

Part Two. Commutative algebra

Chapter 16. Polynomial rings, PIDs, and UFDs

Chapter 17. Field extensions

Chapter 18. Galois theory

Chapter 19. Separability and inseparability

Chapter 20. Cyclotomy and geometric constructions

Chapter 21. Finite fields

Chapter 22. Roots, radicals, and real numbers

Chapter 23. Norms, traces, and discriminants

Chapter 24. Transcendental extensions

Chapter 25. the ArtinSchreier theorem

Chapter 26. Ideal theory

Chapter 27. Noetherian rings

Chapter 28. Integrality

Chapter 29. Dedekind domains

Chapter 30. Algebraic sets and the Nullstellensatz

Unlike similar textbooks, this volume steers away from chapterend problems by including full details of all proofs as problems are presented.
SciTech Book News 
This is a book to be warmly welcomed. The presentation throughout is a model of clarity, and the proofs are precise and complete. The careful reader will learn (much) from it, not only mathematics, but also (and more importantly) how to think mathematically.
Mathematical Reviews 
Isaacs' Algebra, A Graduate Course is a pedagogically important book, to be highly recommended to fledgling algebraists—and every one else, for that matter.
MAA Reviews 
Most of these extra topics are not usually covered in firstyear graduate algebra courses, or in introductory textbooks on modern algebra, but here they are woven into the main text in very natural, effective and instructive a manner, thereby offering a wider panorama of abstract algebra to the interested reader. This profound algebra text will prepare any zealous reader for further steps into one or more of the many branches of algebra, algebraic number theory, or algebraic geometry. Also, it will maintain its wellestablished role as one of the excellent standard texts on the subject, as a highly recommendable source for instructors, and as an utmost valuable companion to the various other great textbooks in the field.
Zentralblatt MATH