Abstract Algebra: The Basic Graduate Year by Robert B. Ash
About this book :-
This is a text for the basic graduate course in abstract algebra, offered by most universities. It covers fundamental algebraic structures (such as groups, rings, fields and modules), and along with maps between these structures. Topics include relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of number theory, geometry, and noncommutative and homological algebra. Its techniques are used in many areas of mathematics, and there are applications to physics, engineering and computer science as well.
The text is written in conventional style, the book can be used as a classroom text or as a reference. Solutions to all problems are included in the text. The text is written in conventional style, the book can be used as a classroom text or as a reference. Applications of abstract algebra are discussed in various fields, including physics, engineering, and computer science.
The book emphasizes intuitive understanding and clarity in proofs, aiming to make complex concepts more accessible. The early chapters provide students with background by investigating the basic properties of groups, rings, fields, and modules. Later chapters examine the relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of algebraic number theory, algebraic geometry, noncommutative algebra, and homological algebra, including categories and functors. An extensive supplement to the text delves much further into homological algebra than most introductory texts, offering applications-oriented results. Solutions to all problems appear in the text. This textbook serves as both a classroom resource and a supplementary reference for students seeking a thorough understanding of abstract algebra.
Book Detail :-
Title:
Abstract Algebra: The Basic Graduate Year by Robert B. Ash
Publisher:
Robert Ash
Year:
2002
Pages:
407
Type:
PDF
Language:
English
ISBN-10 #:
0486453561
ISBN-13 #:
978-0486453569
License:
Linked content owned by author
Amazon:
Amazon
About Author :-
The author
Robert B. Ash
(1935-2015) is a mathematics professor in the Department of Mathematics at the University of Illinois. He was an Assistant Professor in Electrical Engineering at Columbia University and then a Visiting Assistant Professor at the University of California, Berkeley, before coming to the University of Illinois Department of Mathematics in 1963. He retired in 1990. Bob wrote thirteen textbooks but he was most proud of the eight books he posted on his web page during his retirement that were available for free downloading.
Book Contents :-
0. PREREQUISITES
1. GROUP FUNDAMENTALS
2. RING FUNDAMENTALS
3. FIELD FUNDAMENTALS
4. MODULE FUNDAMENTALS
5. SOME BASIC TECHNIQUES OF GROUP THEORY
6. GALOIS THEORY
7. INTRODUCING ALGEBRAIC NUMBER THEORY
8. INTRODUCING ALGEBRAIC GEOMETRY
9. INTRODUCING NONCOMMUTATIVE ALGEBRA
10. INTRODUCING HOMOLOGICAL ALGEBRA
S1. Chain Complexes
S2. The Snake Lemma
S3. The Long Exact Homology Sequence
S4. Projective and Injective Resolutions
S5. Derived Functors
S6. Some Properties of Ext and Tor
S7. Base Change in the Tensor Product
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