Basic modern algebra with applications [electronic resource] / Mahima Ranjan Adhikari, Avishek Adhikari.
2014
QA152.3
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Title
Basic modern algebra with applications [electronic resource] / Mahima Ranjan Adhikari, Avishek Adhikari.
Author
Adhikari, Mahima Ranjan.
ISBN
9788132215998 electronic book
8132215990 electronic book
9788132215981
8132215990 electronic book
9788132215981
Publication Details
New Delhi : Springer, c2014.
Language
English
Description
1 online resource (XIX, 637 pages) : illustrations.
Item Number
10.1007/978-81-322-1599-8
Call Number
QA152.3
Dewey Decimal Classification
512
Summary
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 further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. In addition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to structure theory of rings and homological algebra. Algebraic aspects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraic topology, category theory, algebraic geometry, algebraic number theory, cryptography and theoretical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, with the help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, examples, exercises and historical notes represents a valuable and unique resource.
Note
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 further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. In addition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to structure theory of rings and homological algebra. Algebraic aspects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraic topology, category theory, algebraic geometry, algebraic number theory, cryptography and theoretical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, with the help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, examples, exercises and historical notes represents a valuable and unique resource.
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Access limited to authorized users.
Added Author
Adhikari, Avishek.
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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.
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.