**Progress in Commutative Algebra 2: Closures, Finiteness and Factorization**

by Christopher Francisco, et al.

**Publisher**: De Gruyter Open 2012**ISBN-13**: 9783110278606**Number of pages**: 315

**Description**:

This volume contains surveys on aspects of closure operations, finiteness conditions and factorization. Closure operations on ideals and modules are a bridge between noetherian and nonnoetherian commutative algebra. It contains a nice guide to closure operations by Epstein, but also contains an article on test ideals by Schwede and Tucker and one by Enescu which discusses the action of the Frobenius on finite dimensional vector spaces both of which are related to tight closure.

Download or read it online for free here:

**Download link**

(multiple PDF files)

## Similar books

**A Quick Review of Commutative Algebra**

by

**Sudhir R. Ghorpade**-

**Indian Institute of Technology, Bombay**

These notes 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.

(

**7296**views)

**Introduction to Twisted Commutative Algebras**

by

**Steven V Sam, Andrew Snowden**-

**arXiv**

An expository account of the theory of twisted commutative algebras, which can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate rings of determinantal varieties, etc.

(

**4323**views)

**Frobenius Splitting in Commutative Algebra**

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.

(

**3470**views)

**Commutative Algebra**

by

**Jacob Lurie, Akhil Mathew**-

**Harvard University**

Topics: Unique factorization; Basic definitions; Rings of holomorphic functions; R-modules; Ideals; Localization; SpecR and Zariski topology; The ideal class group; Dedekind domains; Hom and the tensor product; Exactness; Projective modules; etc.

(

**7283**views)