Title

Irreducible divisor graphs in commutative rings with zero divisors

Department/School

Mathematics

Date

6-28-2008

Document Type

Article

Keywords

irreducible divisor graphs, commulative rings, zero-divisors

Abstract

In their article “Irreducible Divisor Graphs”, Coykendall and Maney (2007) introduced the idea of irreducible divisor graphs of elements of a domain. We generalize this concept to commutative rings with zero divisors. In particular, the interplay of unique factoring and connected/complete graphs is explored. The diameter and girth of such graphs are also briefly discussed.

Published in

Communications in Algebra

Citation/Other Information

Axtell, M. & Stickles, J. (2008) Irreducible divisor graphs in commutative rings with zero divisors. Communications in Algebra, 36:5, 1883-1893, DOI: 10.1080/00927870801941473

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