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020			_a9798886130133
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082			_a512 _bREI-A
100			_aReis, Clive
245			_aAbstract algebra : _bintroduction to groups, rings, and fields with applications
250			_a2nd edition
260			_aNew Jersey : _bWorld Scientific, _c2024.
300			_axvii, 555 pages : _billustrations ; _c23 cm
500			_aIncludes index.
520			_aThis second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata. This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya–Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems. Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced — via congruence classes — to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless. In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.
521			_aUndergraduates from approximately 2nd to 4th year. Familarity with linear algebra is required.
650			_aAlgebra, Abstract _vTextbooks
650			_aGroup algebras _vTextbooks
650			_aRings (Algebra) _vTextbooks
650			_aAlgebraic fields _vTextbooks
700			_aRankin, Stuart A.
856			_3Table of content _uhttps://www.worldscientific.com/doi/reader/10.1142/9789814730556_fmatter
856			_3Reviews _uhttps://www.goodreads.com/book/show/28207368-abstract-algebra?ref=nav_sb_ss_1_13#CommunityReviews
942			_2udc _cBK
999			_c35819 _d35819