A Quick Review of Commutative Algebra
by Sudhir R. Ghorpade
Publisher: Indian Institute of Technology, Bombay 2000
Number of pages: 13
These notes attempt to give a rapid review of the rudiments of classical commutative algebra. Some of the main results whose proofs are outlined here are: Hilbert basis theorem, primary decomposition of ideals in noetherian rings, Krull intersection theorem, Going up and Going down theorems for integral extensions, Noether's Normalization Lemma and Hilbert's Nullstellensatz.
Home page url
Download or read it online for free here:
by Ezra Miller - arXiv
This is a survey of lattice point methods for binomial ideals. It is aimed at students and researchers in algebra; it includes many examples, open problems, and elementary introductions to the motivations and background from outside of algebra.
by Tom Marley, Laura Lynch - University of Nebraska - Lincoln
This course is an overview of Homological Conjectures, in particular, the Zero Divisor Conjecture, the Rigidity Conjecture, the Intersection Conjectures, Bass' Conjecture, the Superheight Conjecture, the Direct Summand Conjecture, etc.
by Francis Sowerby Macaulay - Cambridge University Press
Many of the ideas introduced by F.S. Macaulay in this classic book have developed into central concepts in what has become the branch of mathematics known as Commutative Algebra. Today his name is remembered through the term 'Cohen-Macaulay ring'.
by Karen E. Smith, Wenliang Zhang - arXiv
Frobenius splitting has inspired a vast arsenal of techniques in commutative algebra, algebraic geometry, and representation theory. The purpose of these lectures is to give a gentle introduction to Frobenius splitting for beginners.