Download e-book for kindle: A Guide to Groups, Rings, and Fields by Fernando Q. Gouvêa

By Fernando Q. Gouvêa

ISBN-10: 0883853558

ISBN-13: 9780883853559

ISBN-10: 1614442118

ISBN-13: 9781614442110

This advisor bargains a concise assessment of the speculation of teams, jewelry, and fields on the graduate point, emphasizing these facets which are worthwhile in different components of arithmetic. It makes a speciality of the most principles and the way they grasp jointly. it is going to be valuable to either scholars and execs. as well as the traditional fabric on teams, earrings, modules, fields, and Galois idea, the ebook contains discussions of alternative vital issues which are frequently passed over within the typical graduate path, together with linear teams, staff representations, the constitution of Artinian earrings, projective, injective and flat modules, Dedekind domain names, and critical uncomplicated algebras. the entire very important theorems are mentioned, with out proofs yet frequently with a dialogue of the intuitive rules in the back of these proofs. these trying to find how to evaluation and refresh their uncomplicated algebra will reap the benefits of analyzing this advisor, and it'll additionally function a prepared reference for mathematicians who utilize algebra of their paintings.

Show description

Read Online or Download A Guide to Groups, Rings, and Fields PDF

Similar abstract books

Handbook of K-Theory by Eric Friedlander, Daniel R. Grayson PDF

This instruction manual deals a compilation of strategies and leads to K-theory. those volumes encompass chapters, each one of that's devoted to a selected subject and is written by way of a number one specialist. Many chapters current old history; a few current formerly unpublished effects, while a few current the 1st expository account of a subject matter; many talk about destiny instructions in addition to open difficulties.

The q-theory of Finite Semigroups by John Rhodes, Benjamin Steinberg PDF

This accomplished, encyclopedic textual content in 4 components goals to provide the reader — from the graduate scholar to the researcher/practitioner — an in depth figuring out of recent finite semigroup conception, focusing particularly on complex subject matters at the leading edge of analysis. The q-theory of Finite Semigroups provides vital innovations and effects, many for the 1st time in ebook shape, thereby updating and modernizing the semigroup idea literature.

Additional info for A Guide to Groups, Rings, and Fields

Sample text

A; b/ 7! ab, and call the “product of a and b” unless there is risk of confusion. bc/: 17 ✐ ✐ ✐ ✐ ✐ ✐ “master” — 2012/10/2 — 18:45 — page 18 — #36 ✐ ✐ 18 3. Algebraic Structures Associativity implies that there is no ambiguity about the product of n elements of S . In particular, this means that for every a 2 S and every positive integer n we can consider the power an . 1 A semigroup is a set S equipped with an associative operation. It would be hard to say anything generally true about nonassociative operations.

There exists a group G 0 and a (surjective) homomorphism G 0 such that Ker. / D N . WG !

More generally, we can look at the space of all meromorphic functions on H and define a right action of €: if f W H ! z/ D f . z/. The modular functions are invariant under this action, but it turns out to also be relevant to consider other classes of functions that transform in nice ways, known as modular forms. A modular function can be thought of as a meromorphic function on the double coset space Y D €nG=K. The space Y can be made into a (noncompact) Riemann surface. It is the simplest example of a modular curve.

Download PDF sample

A Guide to Groups, Rings, and Fields by Fernando Q. Gouvêa

by Charles

Rated 4.05 of 5 – based on 13 votes