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000696929 020__ $$a9788132215998$$qelectronic book
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000696929 0248_ $$a10.1007/978-81-322-1599-8
000696929 035__ $$aSP(OCoLC)ocn869793340
000696929 035__ $$aSP(OCoLC)869793340
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000696929 050_4 $$aQA152.3
000696929 050_4 $$aQA150-272
000696929 08204 $$a512$$223
000696929 1001_ $$aAdhikari, Mahima Ranjan.
000696929 24510 $$aBasic modern algebra with applications$$h[electronic resource] /$$cMahima Ranjan Adhikari, Avishek Adhikari.
000696929 260__ $$aNew Delhi :$$bSpringer,$$cc2014.
000696929 300__ $$a1 online resource (XIX, 637 pages) :$$billustrations.
000696929 5050_ $$aPrerequisites: Basics of Set Theory and Integers -- Groups: Introductory Concepts -- Actions of Groups, Topological Groups and semigroups -- Rings: Introductory Concepts -- Ideals of Rings: Introductory concepts -- Factorization in Integral Domains and in Polynomial Rings -- Rings with Chain Conditions -- Vector Spaces -- Modules -- Algebraic Aspects of Number Theory -- Algebraic Numbers -- Introduction to Mathematical Cryptography -- Appendix A: Some Aspects of Semirings -- Appendix B: Category Theory -- Appendix C: A Brief Historical Note.
000696929 506__ $$aAccess limited to authorized users.
000696929 5208_ $$aThe book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a way that it encourages independent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. In addition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to structure theory of rings and homological algebra. Algebraic aspects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraic topology, category theory, algebraic geometry, algebraic number theory, cryptography and theoretical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, with the help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, examples, exercises and historical notes represents a valuable and unique resource.
000696929 650_0 $$aAlgebra.
000696929 650_0 $$aGroup theory.
000696929 650_0 $$aNumber theory.
000696929 7001_ $$aAdhikari, Avishek.
000696929 85280 $$bebk$$hSpringerLink
000696929 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-81-322-1599-8$$zOnline Access
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000696929 980__ $$aEBOOK
000696929 980__ $$aBIB
000696929 982__ $$aEbook
000696929 983__ $$aOnline
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