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Algebra = A Teaching and Source Book /
~
Shult, Ernest.
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.
面頁冊數:
XXII, 539 p. 6 illus.online resource. :
Contained By:
Springer Nature eBook
標題:
Associative rings. -
電子資源:
https://doi.org/10.1007/978-3-319-19734-0
ISBN:
9783319197340
Algebra = A Teaching and Source Book /
Shult, Ernest.
Algebra
A Teaching and Source Book /[electronic resource] :by Ernest Shult, David Surowski. - 1st ed. 2015. - XXII, 539 p. 6 illus.online resource.
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
Standard No.: 10.1007/978-3-319-19734-0doiSubjects--Topical Terms:
893564
Associative rings.
LC Class. No.: QA251.5
Dewey Class. No.: 512.46
Algebra = A Teaching and Source Book /
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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.
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