2013/12/28 by Christopher Park Mooney, Mooney, Christopher Park
Mathematics · #13A05 #13E99 #13F15 #5C25 #Advanced Topics in Algebra #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #math.CO #msc:13A05 #msc:13E99 #msc:13F15 #msc:5C25
paper · pdf · doi:10.48550/arxiv.1312.7406
17 pages, 2 figures, to appear in Communications in Algebra
arxiv created 2013/12/28 · openalex publication_date 2013/12/28 · arxiv updated 2014/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1988, I. Beck introduced the notion of a zero-divisor graph of a commutative rings with 1. There have been several generalizations in recent years. In particular, in 2007 J. Coykendall and J. Maney developed the irreducible divisor graph. Much work has been done on generalized factorization, especially τ-factorization. The goal of this paper is to synthesize the notions of τ-factorization and irreducible divisor graphs in domains. We will define a τ-irreducible divisor graph for non-zero non-unit elements of a domain. We show that by studying τ-irreducible divisor graphs, we find equivalent characterizations of several finite τ-factorization properties.