LEADER 05579nam 22009375 450 001 9910300144103321 005 20200701163353.0 010 $a81-322-1599-0 024 7 $a10.1007/978-81-322-1599-8 035 $a(CKB)3710000000078924 035 $a(Springer)9788132215998 035 $a(MH)013884486-0 035 $a(SSID)ssj0001090247 035 $a(PQKBManifestationID)11575644 035 $a(PQKBTitleCode)TC0001090247 035 $a(PQKBWorkID)11134831 035 $a(PQKB)10543801 035 $a(DE-He213)978-81-322-1599-8 035 $a(MiAaPQ)EBC6311664 035 $a(MiAaPQ)EBC1591935 035 $a(Au-PeEL)EBL1591935 035 $a(CaPaEBR)ebr10969048 035 $a(OCoLC)922907541 035 $a(PPN)176126708 035 $a(EXLCZ)993710000000078924 100 $a20131206d2014 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBasic Modern Algebra with Applications$b[electronic resource] /$fby Mahima Ranjan Adhikari, Avishek Adhikari 205 $a1st ed. 2014. 210 1$aNew Delhi :$cSpringer India :$cImprint: Springer,$d2014. 215 $a1 online resource (XIX, 637 p. 48 illus.)$conline resource 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a81-322-1598-2 320 $aIncludes bibliographical references and index. 327 $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. . 330 $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. . 606 $aAlgebra 606 $aCommutative algebra 606 $aCommutative rings 606 $aGroup theory 606 $aNumber theory 606 $aCategories (Mathematics) 606 $aAlgebra, Homological 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 606 $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 606 $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003 615 0$aAlgebra. 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 0$aGroup theory. 615 0$aNumber theory. 615 0$aCategories (Mathematics) 615 0$aAlgebra, Homological. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 14$aAlgebra. 615 24$aCommutative Rings and Algebras. 615 24$aGroup Theory and Generalizations. 615 24$aNumber Theory. 615 24$aCategory Theory, Homological Algebra. 615 24$aApplications of Mathematics. 676 $a512 700 $aAdhikari$b Mahima Ranjan$4aut$4http://id.loc.gov/vocabulary/relators/aut$0957608 702 $aAdhikari$b Avishek$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300144103321 996 $aBasic Modern Algebra with Applications$92504067 997 $aUNINA 999 $aThis Record contains information from the Harvard Library Bibliographic Dataset, which is provided by the Harvard Library under its Bibliographic Dataset Use Terms and includes data made available by, among others the Library of Congress