03133nam a22005055i 4500
978-3-319-19734-0
DE-He213
20180115171635.0
cr nn 008mamaa
150714s2015 gw | s |||| 0|eng d
9783319197340
978-3-319-19734-0
10.1007/978-3-319-19734-0
doi
QA251.5
PBF
bicssc
MAT002010
bisacsh
512.46
23
Shult, Ernest.
author.
Algebra
[electronic resource] :
A Teaching and Source Book /
by Ernest Shult, David Surowski.
Cham :
Springer International Publishing :
Imprint: Springer,
2015.
XXII, 539 p. 6 illus.
online resource.
text
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rdamedia
online resource
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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.
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.
Mathematics.
Algebra.
Associative rings.
Rings (Algebra).
Field theory (Physics).
Group theory.
Mathematics.
Associative Rings and Algebras.
Group Theory and Generalizations.
Field Theory and Polynomials.
Algebra.
Surowski, David.
author.
SpringerLink (Online service)
Springer eBooks
Printed edition:
9783319197333
http://dx.doi.org/10.1007/978-3-319-19734-0
ZDB-2-SMA
371723
371723
0
0
0
0
EBook
elib
elib
2018-01-15
2018-01-15
2018-01-15
EBOOK