000			02370cam a22002655i 4500
001			136445
003			ISI Library, Kolkata
005			20160114153641.0
008			141020s2014 nyu 000 0 eng
020			_a9783319114774
040			_aISI Library
082	0	4	_a512 _223 _bB499
100	1		_aBergman, George M.
245	1	0	_aInvitation to general algebra and universal constructions / _cGeorge M. Bergman.
250			_a2nd ed
260			_aSwitzerland : _bSpringer, _c2014.
300			_ax , 572 p. : _billustrations ; _c24 cm.
490	0		_auniversitext
504			_aIncludes bibliographical references and indexes
505	0		_a1. About the Course, and These Notes -- Part I: Motivation and Examples -- 2. Making Some Things Precise -- 3. Free Groups -- 4. A Cook's Tour of Other Universal Constructions -- Part II: Basic Tools and Concepts -- 5. Ordered Sets, Induction, and the Axiom of Choice -- 6. Lattices, Closure Operators, and Galois Connections -- 7. Categories and Functions -- 8. Universal Constructions in Category - Theoretic Terms -- 9. Varieties of Algebras -- Part III: More on Adjunctions -- 10. Algebra and Coalgebra Objects in Categories, and Functors Having Adjoints -- References -- List of Exercises -- Symbol Index -- Word and Phrase Index.
520			_aThis book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.
650		0	_aAlgebra.
650		0	_aUniversal algebra.
942			_2ddc _cBK
999			_c420440 _d420440