000 | 03773nam a22005775i 4500 | ||
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001 | 978-81-322-1599-8 | ||
003 | DE-He213 | ||
005 | 20160302173449.0 | ||
007 | cr nn 008mamaa | ||
008 | 131206s2014 ii | s |||| 0|eng d | ||
020 |
_a9788132215998 _9978-81-322-1599-8 |
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024 | 7 |
_a10.1007/978-81-322-1599-8 _2doi |
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050 | 4 | _aQA150-272 | |
072 | 7 |
_aPBF _2bicssc |
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072 | 7 |
_aMAT002000 _2bisacsh |
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082 | 0 | 4 |
_a512 _223 |
100 | 1 |
_aAdhikari, Mahima Ranjan. _eauthor. |
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245 | 1 | 0 |
_aBasic Modern Algebra with Applications _h[electronic resource] / _cby Mahima Ranjan Adhikari, Avishek Adhikari. |
264 | 1 |
_aNew Delhi : _bSpringer India : _bImprint: Springer, _c2014. |
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300 |
_aXIX, 637 p. 48 illus. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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505 | 0 | _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. . | |
520 | _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. . | ||
650 | 0 | _aMathematics. | |
650 | 0 | _aAlgebra. | |
650 | 0 | _aCategory theory (Mathematics). | |
650 | 0 | _aHomological algebra. | |
650 | 0 | _aCommutative algebra. | |
650 | 0 | _aCommutative rings. | |
650 | 0 | _aGroup theory. | |
650 | 0 | _aApplied mathematics. | |
650 | 0 | _aEngineering mathematics. | |
650 | 0 | _aNumber theory. | |
650 | 1 | 4 | _aMathematics. |
650 | 2 | 4 | _aAlgebra. |
650 | 2 | 4 | _aCommutative Rings and Algebras. |
650 | 2 | 4 | _aGroup Theory and Generalizations. |
650 | 2 | 4 | _aNumber Theory. |
650 | 2 | 4 | _aCategory Theory, Homological Algebra. |
650 | 2 | 4 | _aApplications of Mathematics. |
700 | 1 |
_aAdhikari, Avishek. _eauthor. |
|
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9788132215981 |
856 | 4 | 0 | _uhttp://dx.doi.org/10.1007/978-81-322-1599-8 |
912 | _aZDB-2-SMA | ||
999 |
_c212161 _d212161 |