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On the Graph of Divisibility of an Integral Domain

Published online by Cambridge University Press:  20 November 2018

Jason Greene Boynton  and
Jim Coykendall
Jason Greene Boynton
Affiliation:
North Dakota State University, Department of Mathematics, Fargo, ND, USA e-mail: jason.boynton@ndsu.edu
Jim Coykendall
Affiliation:
Mathematical Sciences, Clemson University, Martin O-103, Clemson, SC 29634-0975, USA e-mail: jcoyken@clemson.edu
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Abstract

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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

13F1513A05atomicfactorizationdivisibility
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 3 , 01 September 2015 , pp. 449 - 458
Copyright
Copyright © Canadian Mathematical Society 2015

References

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