Algebra 1: Groups, Rings, Fields and Arithmetic

✍ Scribed by Ramji Lal (auth.)

• Publisher: Springer Singapore
• Year: 2017
• Tongue: English
• Leaves: 439
• Series: Infosys Science Foundation Series
• Edition: 1
• Category: Library

✦ Synopsis

This is the first in a series of three volumes dealing with important topics in algebra. It offers an introduction to the foundations of mathematics together with the fundamental algebraic structures, namely groups, rings, fields, and arithmetic. Intended as a text for undergraduate and graduate students of mathematics, it discusses all major topics in algebra with numerous motivating illustrations and exercises to enable readers to acquire a good understanding of the basic algebraic structures, which they can then use to find the exact or the most realistic solutions to their problems.

✦ Table of Contents

Front Matter....Pages i-xvii
Language of Mathematics 1 (Logic)....Pages 1-12
Language of Mathematics 2 (Set Theory)....Pages 13-53
Number System....Pages 55-91
Group Theory....Pages 93-143
Fundamental Theorems....Pages 145-177
Permutation Groups and Classical Groups....Pages 179-217
Elementary Theory of Rings and Fields....Pages 219-268
Number Theory 2....Pages 269-309
Structure Theory of Groups....Pages 311-351
Structure Theory Continued....Pages 353-386
Arithmetic in Rings....Pages 387-419
Back Matter....Pages 421-433

✦ Subjects

Group Theory and Generalizations;Associative Rings and Algebras;Non-associative Rings and Algebras;Commutative Rings and Algebras;Field Theory and Polynomials;Number Theory