Basic Modern Algebra with Applications

• Main Authors: Adhikari, Mahima Ranjan (Author), Adhikari, Avishek (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New Delhi : Springer India : Imprint: Springer, 2014.
• Subjects: Mathematics.; Algebra.; Category theory (Mathematics).; Homological algebra.; Commutative algebra.; Commutative rings.; Group theory.; Applied mathematics.; Engineering mathematics.; Number theory.; Commutative Rings and Algebras.; Group Theory and Generalizations.; Number Theory.; Category Theory, Homological Algebra.; Applications of Mathematics.

The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a way that it encourages independent thinking and motivates students towards...

Table of Contents:

• Prerequisites: Basics of Set Theory and Integers
• Groups: Introductory Concepts
• Actions of Groups, Topological Groups and semigroups
• Rings: Introductory Concepts
• Ideals of Rings: Introductory concepts
• Factorization in Integral Domains and in Polynomial Rings
• Rings with Chain Conditions
• Vector Spaces
• Modules
• Algebraic Aspects of Number Theory
• Algebraic Numbers
• Introduction to Mathematical Cryptography
• Appendix A: Some Aspects of Semirings
• Appendix B: Category Theory
• Appendix C: A Brief Historical Note. .