1. CMB Online first
|On the Graph of Divisibility of an Integral Domain|
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.
Keywords:atomic, factorization, divisibility
2. CMB 2000 (vol 43 pp. 362)
|Examples of Half-Factorial Domains |
In this paper, we determine some sufficient conditions for an $A + XB[X]$ domain to be an HFD. As a consequence we give new examples of HFDs of the type $A + XB[X]$.
Keywords:atomic domain, HFD
Categories:13A05, 13B30, 13F15, 13G05