Jordan–Hölder, modularity and distributivity in non-commutative algebra

Non-commutative combinatorial algebra

Commutative Algebra Commutative Algebra : General

Non-commutative Hopf algebra of formal diffeomorphisms

The subject of this paper are two Hopf algebras which are the non-commutative analogues of two different groups of formal power series. The first group is the set of invertible series with the group law being multiplication of series, while the second group is the set of formal diffeomorphisms with the group law being composition of series. The motivation to introduce these Hopf algebras comes ...

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...