000			03536nam a22005055i 4500
001			978-81-322-1599-8
003			DE-He213
005			20140220082526.0
007			cr nn 008mamaa
008			131206s2014 ii | s |||| 0|eng d
020			_a9788132215998 _9978-81-322-1599-8
024	7		_a10.1007/978-81-322-1599-8 _2doi
050		4	_aQA150-272
072		7	_aPBF _2bicssc
072		7	_aMAT002000 _2bisacsh
082	0	4	_a512 _223
100	1		_aAdhikari, Mahima Ranjan. _eauthor.
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.
300			_aXIX, 637 p. 48 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
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	_aGroup theory.
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			_c93758 _d93758