# Publication list for Rotman, Joseph

## Latest Titles

• Base Product Code Keyword List: gsm; GSM; gsm/180; GSM/180; gsm-180; GSM-180
Print Product Code: GSM/180
Online Product Code: GSM/180.E
Title (HTML): Advanced Modern Algebra: Third Edition, Part 2
Author(s) (Product display): Joseph J. Rotman
Affiliation(s) (HTML): University of Illinois at Urbana-Champaign, Urbana, IL
Abstract:

This book is the second part of the new edition of Advanced Modern Algebra (the first part published as Graduate Studies in Mathematics, Volume 165). Compared to the previous edition, the material has been significantly reorganized and many sections have been rewritten. The book presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.

Book Series Name: Graduate Studies in Mathematics
Volume: 180
Publication Month and Year: 2017-08-15
Copyright Year: 2017
Page Count: 558
Cover Type: Hardcover
Print ISBN-13: 978-1-4704-2311-7
Online ISBN 13: 978-1-4704-4170-8
Print ISSN: 1065-7339
Online ISSN: 1065-7339
Primary MSC: 12; 13; 14; 15; 16; 18; 20
Textbook?: true
Applied Math?: false
Electronic Media?: false
Apparel or Gift: false
SXG Subject: AA
Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/gsm-180
Online Price 1 Label: List
Online Price 1: 94.00
Print Price 1 Label: List
Print Price 1: 94.00
Online Price 2 Label: Individual Member
Online Price 2: 75.20
Print Price 2 Label: Individual Member
Print Price 2: 75.20
Dual Price 1 Label: List
Dual Price 1: 117.5
Dual Price 2 Label: Individual Member
Dual Price 2: 94
Print Add to Cart URL: /some/url/at/AMS/GSM-180
Electronic Add to Cart URL: /some/url/at/AMS/GSM-180.E
Exam/Desk Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-4170-8&pisbn=978-1-4704-2311-7&epc=GSM/180.E&ppc=GSM/180&title=Advanced%20Modern%20Algebra%3A%20Third%20Edition%2C%20Part%202&author=Joseph%20J.%20Rotman&type=DE
Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-4170-8&pisbn=978-1-4704-2311-7&epc=GSM/180.E&ppc=GSM/180&title=Advanced%20Modern%20Algebra%3A%20Third%20Edition%2C%20Part%202&author=Joseph%20J.%20Rotman&type=R
Sets and Parts:

#### This item is also available as part of a set:

Readership:

Graduate students and researchers interested in learning and teaching algebra.

Reviews:

This is a good book and a fitting tribute to a great mathematical expositor. I'll keep both the second edition and the two parts of the third edition on my shelf, and I'm sure I'll turn to them often in the future.

-- Fernando Q. Gouvêa, MAA Reviews

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Cover Image URL: ~~FreeAttachments/gsm-180-cov.jpg
• Base Product Code Keyword List: gsm; GSM; gsm/165; GSM/165; gsm-165; GSM-165; gsm/165/180; GSM/165/180; gsm-165-180; GSM-165-180
Print Product Code: GSM/165/180
Title (HTML): Advanced Modern Algebra: Third Edition, Parts 1 and 2
Author(s) (Product display): Joseph J. Rotman
Affiliation(s) (HTML): University of Illinois at Urbana-Champaign, Urbana, IL
Abstract:

This new edition, now in two parts, has been significantly reorganized and many sections have been rewritten. The first part, designed for a first year of graduate algebra, consists of two courses: Galois theory and Module theory. Topics covered in the first course are classical formulas for solutions of cubic and quartic equations, classical number theory, commutative algebra, groups, and Galois theory. Topics in the second course are Zorn's lemma, canonical forms, inner product spaces, categories and limits, tensor products, projective, injective, and flat modules, multilinear algebra, affine varieties, and Gröbner bases.

The second part presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.

Book Series Name: Graduate Studies in Mathematics
Publication Month and Year: 2017-08-29
Copyright Year: 2017
Cover Type: Hardcover
Print ISBN-13: 978-1-4704-4174-6
Print ISSN: 1065-7339
Primary MSC: 12; 13; 14; 15; 16; 18; 20
Textbook?: true
Applied Math?: false
Home Page?: false
Sample?: false
Reference?: false
Electronic Media?: false
Apparel or Gift: false
SXG Subject: AA
Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/gsm-165
Print Price 1 Label: List
Print Price 1: 174.00
Print Price 2 Label: Individual Member
Print Price 2: 139.20
Print Add to Cart URL: /some/url/at/AMS/GSM-165-180
Exam/Desk Copy: http://www.ams.org/exam-desk-review-request?&pisbn=978-1-4704-4174-6&ppc=GSM/165/180&title=Advanced%20Modern%20Algebra%3A%20Third%20Edition%2C%20Parts%201%20and%202&author=Joseph%20J.%20Rotman&type=DE
Review Copy: http://www.ams.org/exam-desk-review-request?&pisbn=978-1-4704-4174-6&ppc=GSM/165/180&title=Advanced%20Modern%20Algebra%3A%20Third%20Edition%2C%20Parts%201%20and%202&author=Joseph%20J.%20Rotman&type=R
Sets and Parts:

#### Item(s) contained in this set are available for individual sale:

Readership:

Graduate students and researchers interested in learning and teaching algebra.

Cover Image URL: ~~FreeAttachments/gsm-165-180-cov.jpg
• Base Product Code Keyword List: gsm; GSM; gsm/165; GSM/165; gsm-165; GSM-165
Print Product Code: GSM/165
Online Product Code: GSM/165.E
Title (HTML): Advanced Modern Algebra: Third Edition, Part 1
Author(s) (Product display): Joseph J. Rotman
Affiliation(s) (HTML): University of Illinois at Urbana-Champaign, Urbana, IL
Abstract:

This new edition, now in two parts, has been significantly reorganized and many sections have been rewritten. This first part, designed for a first year of graduate algebra, consists of two courses: Galois theory and Module theory. Topics covered in the first course are classical formulas for solutions of cubic and quartic equations, classical number theory, commutative algebra, groups, and Galois theory. Topics in the second course are Zorn's lemma, canonical forms, inner product spaces, categories and limits, tensor products, projective, injective, and flat modules, multilinear algebra, affine varieties, and Gröbner bases.

Book Series Name: Graduate Studies in Mathematics
Volume: 165
Publication Month and Year: 2015-11-30
Copyright Year: 2015
Page Count: 706
Cover Type: Hardcover
Print ISBN-13: 978-1-4704-1554-9
Online ISBN 13: 978-1-4704-2731-3
Print ISSN: 1065-7339
Online ISSN: 1065-7339
Primary MSC: 12; 13; 14; 15; 16; 18; 20
Textbook?: true
Applied Math?: false
Home Page?: false
Sample?: false
Reference?: false
Electronic Media?: false
Apparel or Gift: false
SXG Subject: AA
Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/gsm-165
Online Price 1 Label: List
Online Price 1: 89.00
Print Price 1 Label: List
Print Price 1: 89.00
Online Price 2 Label: Individual Member
Online Price 2: 71.20
Print Price 2 Label: Individual Member
Print Price 2: 71.20
Dual Price 1 Label: List
Dual Price 1: 111.25
Dual Price 2 Label: Individual Member
Dual Price 2: 89
Print Add to Cart URL: /some/url/at/AMS/GSM-165
Electronic Add to Cart URL: /some/url/at/AMS/GSM-165.E
Exam/Desk Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-2731-3&pisbn=978-1-4704-1554-9&epc=GSM/165.E&ppc=GSM/165&title=Advanced%20Modern%20Algebra%3A%20Third%20Edition%2C%20Part%201&author=Joseph%20J.%20Rotman&type=DE
Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-2731-3&pisbn=978-1-4704-1554-9&epc=GSM/165.E&ppc=GSM/165&title=Advanced%20Modern%20Algebra%3A%20Third%20Edition%2C%20Part%201&author=Joseph%20J.%20Rotman&type=R
Sets and Parts:

#### This item is also available as part of a set:

Readership:

Graduate students and researchers interested in learning and teaching algebra.

Reviews:

The organization of the text is clear and the pace is leisurely...recently I taught the second part of a first-year graduate course in algebra, and in the process dipped into this book at various points. I enjoyed the presentation, and the commentary on constructions and results aimed to place them in context, and I found the numerous examples and exercises helpful. I will be using this book when teaching such courses again, if not always as the main text, certainly as a useful supplement.

-- Srikanth B. Iyengar, Mathematical Reviews

Rotman is a wonderful expositor, and the two courses in this book strike me as well thought out and well presented.

-- Fernando Q. Gouvêa, MAA

Related Products:
Cover Image URL: ~~FreeAttachments/gsm-165-cov.jpg
• Base Product Code Keyword List: gsm; GSM; gsm/114; GSM/114; gsm-114; GSM-114
Online Product Code: GSM/114.E
Title (HTML): Advanced Modern Algebra: Second Edition
Author(s) (Product display): Joseph J. Rotman
Abstract:

This book is designed as a text for the first year of graduate algebra, but it can also serve as a reference since it contains more advanced topics as well. This second edition has a different organization than the first. It begins with a discussion of the cubic and quartic equations, which leads into permutations, group theory, and Galois theory (for finite extensions; infinite Galois theory is discussed later in the book). The study of groups continues with finite abelian groups (finitely generated groups are discussed later, in the context of module theory), Sylow theorems, simplicity of projective unimodular groups, free groups and presentations, and the Nielsen–Schreier theorem (subgroups of free groups are free).

The study of commutative rings continues with prime and maximal ideals, unique factorization, noetherian rings, Zorn's lemma and applications, varieties, and Gröbner bases. Next, noncommutative rings and modules are discussed, treating tensor product, projective, injective, and flat modules, categories, functors, and natural transformations, categorical constructions (including direct and inverse limits), and adjoint functors. Then follow group representations: Wedderburn–Artin theorems, character theory, theorems of Burnside and Frobenius, division rings, Brauer groups, and abelian categories. Advanced linear algebra treats canonical forms for matrices and the structure of modules over PIDs, followed by multilinear algebra.

Homology is introduced, first for simplicial complexes, then as derived functors, with applications to Ext, Tor, and cohomology of groups, crossed products, and an introduction to algebraic $$K$$-theory. Finally, the author treats localization, Dedekind rings and algebraic number theory, and homological dimensions. The book ends with the proof that regular local rings have unique factorization.

Book Series Name: Graduate Studies in Mathematics
Volume: 114
Publication Month and Year: 2010-08-11
Copyright Year: 2010
Page Count: 1008
Online ISBN 13: 978-1-4704-1176-3
Online ISSN: 1065-7339
Primary MSC: 11; 12; 13; 15; 16; 18; 19; 20
Textbook?: true
Applied Math?: false
Home Page?: false
Sample?: false
Reference?: false
Electronic Media?: false
Apparel or Gift: false
SXG Subject: AA
Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/gsm-114
Online Price 1 Label: List
Online Price 1: 99.00
Online Price 2 Label: Individual Member
Online Price 2: 79.20
Electronic Add to Cart URL: /some/url/at/AMS/GSM-114.E
Exam/Desk Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1176-3&epc=GSM/114.E&title=Advanced%20Modern%20Algebra%3A%20Second%20Edition&author=Joseph%20J.%20Rotman&type=DE
Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1176-3&epc=GSM/114.E&title=Advanced%20Modern%20Algebra%3A%20Second%20Edition&author=Joseph%20J.%20Rotman&type=R