On the graph of divisibility of an integral domain

Abstract

It is well-known that the factorization properties of a domain are reflected in the structure of its group of divisibility. The main theme of this paper is to introduce a topological/graph-theoretic point of view to the current understanding of factorization in integral domains. We also show that connectedness properties in the graph and topological space give rise to a generalization of atomicity.

9 pages

Cited by in corpus (3)

• On the atomic structure of torsion-free monoids
• Classifying Subatomic Domains
• A Homological Approach to Factorization