TY  - BOOK
AU  - Adhikari,Mahima Ranjan
AU  - Adhikari,Avishek
ED  - SpringerLink (Online service)
TI  - Basic Modern Algebra with Applications
SN  - 9788132215998
AV  - QA150-272 
U1  - 512 23
PY  - 2014///
CY  - New Delhi
PB  - Springer India, Imprint: Springer
KW  - Mathematics
KW  - Algebra
KW  - Category theory (Mathematics)
KW  - Homological algebra
KW  - Commutative algebra
KW  - Commutative rings
KW  - Group theory
KW  - Applied mathematics
KW  - Engineering mathematics
KW  - Number theory
KW  - Commutative Rings and Algebras
KW  - Group Theory and Generalizations
KW  - Number Theory
KW  - Category Theory, Homological Algebra
KW  - Applications of Mathematics
N1  - 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.
N2  - 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.
UR  - http://dx.doi.org/10.1007/978-81-322-1599-8
ER  -