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Algebra = a teaching and source book /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Algebra/ by Ernest Shult, David Surowski.
其他題名:	a teaching and source book /
作者:	Shult, Ernest.
其他作者:	Surowski, David.
出版者:	Cham :Springer International Publishing : : 2015.,
面頁冊數:	xxii, 539 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Algebra. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-19734-0
ISBN:	9783319197340 (electronic bk.)

Algebra = a teaching and source book /
Shult, Ernest.

Algebraa teaching and source book /[electronic resource] :by Ernest Shult, David Surowski. - Cham :Springer International Publishing :2015. - xxii, 539 p. :ill., digital ;24 cm.

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.

ISBN: 9783319197340 (electronic bk.)

Standard No.: 10.1007/978-3-319-19734-0doiSubjects--Topical Terms:

579870
Algebra.

LC Class. No.: QA152.3

Dewey Class. No.: 512

Algebra = a teaching and source book /
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505 0 $a 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.
520 $a 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.
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