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＜電子ブック＞
Abstract Algebra / by Pierre Antoine Grillet
(Graduate Texts in Mathematics. ISSN:21975612 ; 242)

版	2nd ed. 2007.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2007
本文言語	英語
大きさ	XII, 674 p : online resource
著者標目	*Grillet, Pierre Antoine author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Associative rings LCSH:Associative algebras LCSH:Group theory FREE:Algebra FREE:Associative Rings and Algebras FREE:Group Theory and Generalizations
一般注記	Groups -- Structure of Groups -- Rings -- Field Extensions -- Galois Theory -- Fields with Orders or Valuations -- Commutative Rings -- Modules -- Semisimple Rings and Modules -- Projectives and Injectives -- Constructions -- Ext and Tor -- Algebras -- Lattices -- Universal Algebra -- Categories "Abstract Algebra" is a clearly written, self-contained basic algebra text for graduate students, with a generous amount of additional material that suggests the scope of contemporary algebra. The first chapters blend standard contents with a careful introduction to proofs with arrows. The last chapters, on universal algebras and categories, including tripleability, give valuable general views of algebra. There are over 1400 exercises, at varying degrees of difficulty. For the new edition, the author has completely rewritten the entire text, streamlining the first chapters for rapid access to Galois theory, removing some material, and adding introductions to Groebner bases, Ext and Tor, and other topics. From a review of the First Edition: ...combines an exceptionally accessible discussion of the basic material with a just as thorough and well-organized treatment of the many additional (advanced) topics included.... represents an outstanding introduction to modern abstract algebra as a whole, with many unique features. It captivates the reader by its remarkable diversity, comprehensiveness, elegant succinctness, and coherence. - Werner Kleinert, Zentralblatt HTTP:URL=https://doi.org/10.1007/978-0-387-71568-1

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