大葉大學圖書館 |

An invitation to general algebra and universal constructions[electronic resource] /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	512
書名/作者:	An invitation to general algebra and universal constructions/ by George M. Bergman.
作者:	Bergman, George M.
出版者:	Cham : : Springer International Publishing :, 2015.
面頁冊數:	x, 572 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Algebra.
標題:	Algebra, Universal.
標題:	Mathematics.
標題:	General Algebraic Systems.
標題:	Category Theory, Homological Algebra.
標題:	Associative Rings and Algebras.
ISBN:	9783319114781 (electronic bk.)
ISBN:	9783319114774 (paper)
內容註:	1 About the course, and these notes -- Part I: Motivation and Examples -- 2 Making Some Things Precise -- 3 Free Groups -- 4 A Cook's Tour -- 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 Functors -- 8 Universal Constructions -- 9 Varieties of Algebras -- Part III: More on Adjunctions -- 10 Algebras, Coalgebras, and Adjunctions -- References -- List of Exercises -- Symbol Index -- Word and Phrase Index.
摘要、提要註:	Rich in examples and intuitive discussions, this 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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-11478-1

An invitation to general algebra and universal constructions[electronic resource] /
Bergman, George M.

An invitation to general algebra and universal constructions[electronic resource] /by George M. Bergman. - 2nd ed. - Cham :Springer International Publishing :2015. - x, 572 p. :ill., digital ;24 cm. - Universitext,0172-5939. - Universitext..

1 About the course, and these notes -- Part I: Motivation and Examples -- 2 Making Some Things Precise -- 3 Free Groups -- 4 A Cook's Tour -- 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 Functors -- 8 Universal Constructions -- 9 Varieties of Algebras -- Part III: More on Adjunctions -- 10 Algebras, Coalgebras, and Adjunctions -- References -- List of Exercises -- Symbol Index -- Word and Phrase Index.

Rich in examples and intuitive discussions, this 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.

ISBN: 9783319114781 (electronic bk.)

Standard No.: 10.1007/978-3-319-11478-1doiSubjects--Topical Terms:

189734
Algebra.

LC Class. No.: QA150

Dewey Class. No.: 512

An invitation to general algebra and universal constructions[electronic resource] /
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