Connection between commutative algebra and topology

Commutative Algebra Commutative Algebra : General

Elements in a Commutative Banach Algebra Determining the Norm Topology

For an element a of a commutative complex Banach algebra (A, ‖ · ‖) we investigate the following property: every complete norm | · | on A making the multiplication by a from (A, | · |) to itself continuous is equivalent to ‖ · ‖.

Commutative Algebra

Introduction 5 0.1. What is Commutative Algebra? 5 0.2. Why study Commutative Algebra? 5 0.3. Acknowledgments 7 1. Commutative rings 7 1.1. Fixing terminology 7 1.2. Adjoining elements 10 1.3. Ideals and quotient rings 11 1.4. The monoid of ideals of R 14 1.5. Pushing and pulling ideals 15 1.6. Maximal and prime ideals 16 1.7. Products of rings 17 1.8. A cheatsheet 19 2. Galois Connections 20 2...

Cycles and Commutative Algebra

The aim of this article is to describe several applications of the theory of cycles to problems in Commutative Algebra. The main topic is the use of the theory of local Chern characters defined in the Chow group of a ring to answer some questions on modules of finite homological dimension and to clarify others. In the first section, we describe the origins of these problems in Intersection Theo...

Connection between Space-Time Supersymmetry and Non-Commutative Geometry

The non-commutative geometric construction of A. Connes [1-5] has been successful in giving a geometrical interpretation of the standard model as well as some grand unification models. Our lack of ability to quantize the non-commutative actions forced on us to quantize the classical actions resulting from the non-commutative ones by adopting the usual rules. The symmetries that might be present...