Algebra in Action A Course in Groups Rings and Fields 1st Edition by Shahriar Shahriari 9781470428495 1470428490

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ISBN 10:1470428490 
ISBN 13:9781470428495
Author:Shahriar Shahriari

Provides a readable, student-friendly, and somewhat sophisticated introduction to abstract algebra. It is aimed at sophomore or junior undergraduates who are seeing the material for the first time. In addition to the usual definitions and theorems, there is ample discussion to help students build intuition and learn how to think about the abstract concepts.

Algebra in Action A Course in Groups Rings and Fields 1st Table of contents:

(Mostly finite) group theory: Four basic examples

 Groups: The basics The alternating groups

Group actions 

A subgroup acts on the group:

Cosets and Lagrange’s theorem

A group acts on itself:

Counting and the conjugation of action

 Acting on subsets, cosets, and subgroups:

The Sylow theorems 

Counting the number of orbits The lattice of subgroups

 Acting on its subgroups:

Normal subgroups and quotient groups

Group homomorphisms 

Using Sylow theorems to analyze finite groups

 Direct and semidirect products

Solvable and nilpotent groups (Mostly commutative) ring theory:

Rings Homomorphisms, ideals, and quotient rings 

Field of fractions and localization

Factorization, EDs, PIDs, and UFDs 

Polynomial rings Gaussian integers and (a little) number theory

 Field and Galois theory: Introducing field theory and Galois theory

Field extensions 

Straightedge and compass constructions

Splitting fields and Galois groups Galois, normal, and separable extensions

Fundamental theorem of Galois theory Finite fields and cyclotomic extensions

Radical extensions, solvable groups, and the quintic Hints for selected problems

 Short answers for selected problems

Complete solutions for selected (odd-numbered) problems

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Shahriar Shahriari,Groups,Action,Algebra