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1 |
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|a Bergman, George M.,
|d 1943-
|1 https://id.oclc.org/worldcat/entity/E39PBJmDhCDgvpfhf746jTkRrq,
|e author.
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| 245 |
1 |
3 |
|a An invitation to general algebra and universal constructions /
|c George M. Bergman.
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| 250 |
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|a Second edition.
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| 264 |
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|a Cham :
|b Springer,
|c 2015.
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| 300 |
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|a 1 online resource (x, 572 pages) :
|b illustrations.
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| 336 |
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|a text
|b txt
|2 rdacontent.
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| 337 |
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|a computer
|b c
|2 rdamedia.
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| 338 |
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|a online resource
|b cr
|2 rdacarrier.
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| 347 |
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|a text file
|b PDF
|2 rda.
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| 490 |
1 |
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|a Universitext ;
|v 351.
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| 504 |
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|a Includes bibliographical references and indexes.
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|a Print version record.
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| 520 |
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|a Rich in examples and intuitive discussions, this book presents General Algebra using the unifying view of categories and functors. Beginning with a study, in non-category-theoretic terms, of many familiar and not-so-familiar constructs in algebra (plus two from topology for perspective), the reader is guided toward understanding and appreciating the general concepts and tools that unify these constructs. . Topics include: set theory, lattices, category theory, formulation of universal constructions in terms of category theory, varieties of algebras and adjunctions. A large number of exercises, from the routine to the challenging, interspersed throughout the text, develop the reader's understanding of the material, exhibit applications of general theory to various areas of algebra, and, in some cases, point out open questions. outstanding. Graduate students and researchers who wish to become fluent in important mathematical constructs will appreciate this carefully motivated book.
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|a 1 About the course and these notes -- Part I: Motivation and examples -- 2 How to do some things precisely -- 3 Free groups -- 4 A cook's tour -- Part II: Tools and basics -- 5 Sets orders, 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 about conjunctions - 10 algebras, coalgebras and complements - References - List of exercises - Index of symbols - Index of words and phrases.
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|a English.
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|a Algebra.
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| 650 |
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|a Algebra, Universal.
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| 650 |
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|a Mathematics.
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| 650 |
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2 |
|a Mathematics.
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|a Algèbre.
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|a Algèbre universelle.
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| 650 |
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|a Mathématiques.
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| 650 |
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|a Mathematical foundations.
|2 bicssc.
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| 650 |
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|a Algebra.
|2 bicssc.
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| 650 |
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7 |
|a algebra.
|2 aat.
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| 650 |
|
7 |
|a Mathematics
|x Algebra
|x Abstract.
|2 bisacsh.
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| 650 |
|
7 |
|a Álgebra universal.
|2 embne.
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| 650 |
|
7 |
|a Matemáticas.
|2 embne.
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| 650 |
|
7 |
|a Álgebra.
|2 embne.
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| 650 |
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7 |
|a Mathematics.
|2 fast.
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| 650 |
|
7 |
|a Algebra.
|2 fast.
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| 650 |
|
7 |
|a Algebra, Universal.
|2 fast.
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| 710 |
2 |
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|a SpringerLink (Online service)
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0 |
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|t Springer eBooks.
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| 776 |
0 |
8 |
|i Print version:
|a Bergman, George M.
|t Invitation to General Algebra and Universal Constructions.
|b 0002 2015
|z 3319114778
|w (OCoLC)898455317.
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