product iamge

Groups, Rings and Modules

This document was uploaded by one of our users. The uploader already confirmed that they had the permission to publish it. If you are author/publisher or own the copyright of this documents, please report to us by using this DMCA report form.

Download
Search on Amazon

Simply click on the Download Book button.

Yes, Book downloads on Ebookily are 100% Free.

Sometimes the book is free on Amazon As well, so go ahead and hit "Search on Amazon"

Author(s): O. Randal-Williams, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part IB Lecture Notes
Publisher: University of Cambridge
Year: 2016

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; algebra; abstract algebra; modern algebra; group theory; ring theory; module; fields; field theory

Introduction
Groups
Basic concepts
Normal subgroups, quotients, homomorphisms, isomorphisms
Actions of permutations
Conjugacy, centralizers and normalizers
Finite p-groups
Finite abelian groups
Sylow theorems
Rings
Definitions and examples
Homomorphisms, ideals, quotients and isomorphisms
Integral domains, field of factions, maximal and prime ideals
Factorization in integral domains
Factorization in polynomial rings
Gaussian integers
Algebraic integers
Noetherian rings
Modules
Definitions and examples
Direct sums and free modules
Matrices over Euclidean domains
Modules over F[X] and normal forms for matrices
Conjugacy of matrices*
Index