Algebra
A Teaching and Source Book
Shult, Ernest.
creator
author.
Surowski, David.
author.
SpringerLink (Online service)
text
gw
2015
monographic
eng
access
XXII, 539 p. 6 illus. online resource.
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.
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.
by Ernest Shult, David Surowski.
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
QA251.5
512.46
Springer eBooks
9783319197340
http://dx.doi.org/10.1007/978-3-319-19734-0
http://dx.doi.org/10.1007/978-3-319-19734-0
150714
20180115171635.0
978-3-319-19734-0