عنوان

Algebra :A Teaching and Source Book

شابک

9783319197340

زبان متن نوشتاري يا گفتاري و مانند آن

انگلیسی

عنوان اصلي

Algebra :A Teaching and Source Book

نام نخستين پديدآور

by Ernest Shult, David Surowski.

وضعيت ويراست

1st ed. 2015.

محل نشرو پخش و غیره

Cham :

نام ناشر، پخش کننده و غيره

Imprint: Springer,

تاریخ نشرو بخش و غیره

2015.

نام خاص و کميت اثر

1 online resource (XXII, 539 pages 6 illustrations)

متن يادداشت

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.

بدون عنوان

0

متن يادداشت

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.

عنصر شناسه ای

Algebra.

عنصر شناسه ای

Field theory (Physics).

عنصر شناسه ای

Group theory.

عنصر شناسه ای

Rings (Algebra).

عنصر شناسه ای

Associative Rings and Algebras.

عنصر شناسه ای

Field Theory and Polynomials.

عنصر شناسه ای

Group Theory and Generalizations.

شماره

نشانه اثر

ويراست

عنصر شناسه اي

Shult, Ernest,

عنصر شناسه اي

Surowski, David,

تاريخ عمليات

20221107173307.0

قواعد فهرست نويسي ( بخش توصيفي )

rda

نوع ماده

BL

کد کاربرگه

270410

تكميل شده

Y