
Advanced Modern Algebra
Third Edition, Parts 1 and 2
Joseph J. Rotman(Author)
American Mathematical Society (Publisher)
Published on 30. August 2017
Book
Hardback
1264 pages
978-1-4704-4174-6 (ISBN)
Description
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 Grobner 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.
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 229 mm
Width: 152 mm
ISBN-13
978-1-4704-4174-6 (9781470441746)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
Joseph J. Rotman, University of Illinois at Urbana-Champaign, IL.
Content
Contents for Part 1:
Course I: Classical formulas
Classical number theory
Commutative rings
Groups
Galois theory
Appendix: Set theory
Appendix: Linear algebra
Course II: Modules
Zorn's lemma
Advanced linear algebra
Categories of modules
Multilinear algebra
Commutative algebra II
Appendix: Categorical limits
Appendix: Topological spaces
Bibliography
Special notation
Index
Contents for Part 2: More groups
Representation theory
Homology
More categories
Commutative rings III
Bibliography
Index.
Course I: Classical formulas
Classical number theory
Commutative rings
Groups
Galois theory
Appendix: Set theory
Appendix: Linear algebra
Course II: Modules
Zorn's lemma
Advanced linear algebra
Categories of modules
Multilinear algebra
Commutative algebra II
Appendix: Categorical limits
Appendix: Topological spaces
Bibliography
Special notation
Index
Contents for Part 2: More groups
Representation theory
Homology
More categories
Commutative rings III
Bibliography
Index.