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On the Graph of Divisibility of an Integral Domain

  Published:2015-05-21
 Printed: Sep 2015
  • Jason Greene Boynton,
    North Dakota State University, Department of Mathematics, Fargo, ND, USA
  • Jim Coykendall,
    Mathematical Sciences, Clemson University, Martin O-103, Clemson, SC 29634-0975, USA
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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.
Keywords: atomic, factorization, divisibility atomic, factorization, divisibility
MSC Classifications: 13F15, 13A05 show english descriptions Rings defined by factorization properties (e.g., atomic, factorial, half-factorial) [See also 13A05, 14M05]
Divisibility; factorizations [See also 13F15]
13F15 - Rings defined by factorization properties (e.g., atomic, factorial, half-factorial) [See also 13A05, 14M05]
13A05 - Divisibility; factorizations [See also 13F15]
 

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