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＜電子ブック＞
Algebra : A Teaching and Source Book / by Ernest Shult, David Surowski

版	1st ed. 2015.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2015
大きさ	XXII, 539 p. 6 illus : online resource
著者標目	*Shult, Ernest author Surowski, David author SpringerLink (Online service)
件　名	LCSH:Associative rings LCSH:Associative algebras LCSH:Group theory LCSH:Algebraic fields LCSH:Polynomials LCSH:Algebra FREE:Associative Rings and Algebras FREE:Group Theory and Generalizations FREE:Field Theory and Polynomials FREE:Algebra
一般注記	Basics -- Basic Combinatorial Principles of Algebra -- Review of Elementary Group Properties -- Permutation Groups and Group Actions -- Normal Structure of Groups -- Generation in Groups -- Elementary Properties of Rings -- Elementary properties of Modules -- The Arithmetic of Integral Domains -- Principal Ideal Domains and Their Modules -- Theory of Fields -- Semiprime Rings -- Tensor Products This book presents a graduate-level course on modern algebra. It can be used as a teaching book – owing to the copious exercises – and as a source book for those who wish to use the major theorems of algebra. The course begins with the basic combinatorial principles of algebra: posets, chain conditions, Galois connections, and dependence theories. Here, the general Jordan–Holder Theorem becomes a theorem on interval measures of certain lower semilattices. This is followed by basic courses on groups, rings and modules; the arithmetic of integral domains; fields; the categorical point of view; and tensor products. Beginning with introductory concepts and examples, each chapter proceeds gradually towards its more complex theorems. Proofs progress step-by-step from first principles. Many interesting results reside in the exercises, for example, the proof that ideals in a Dedekind domain are generated by at most two elements. The emphasis throughout is on real understanding as opposed to memorizing a catechism and so some chapters offer curiosity-driven appendices for the self-motivated student HTTP:URL=https://doi.org/10.1007/978-3-319-19734-0

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