Comaximal factorization graphs in integral domains

SHAFIQ UR REHMAN

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Comaximal factorization graphs in integral domains

Author(s)

SHAFIQ UR REHMAN Department of Mathematics, COMSATS Institute of Information Technology, Attock, Pakistan.

Abstract

In [1], I. Beck introduced the idea of a zero divisor graph of a commutative ring and later in [2], J. Coykendall and J. Maney generalized this idea to study factorization in integral domains. They defined irreducible divisor graphs and used these irreducible divisor graphs to characterize UFDs. We define comaximal factorization graphs and use these graphs to characterize UCFDs defined in [3]. We also study that, in certain cases, comaximal factorization graph is formed by joining r copies of the complete graph Km with one copy of complete graph Kn in common.

Publication Details

Page(s) 65-71

DOI DOI not available

Published Journal: Journal of Prime Research in Mathematics, Volume: 9, Issue: 1, Year: 2013

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Keywords

factorization, Complete Graph, AMS SUBJECT, 05C99, integral domain, 13A05, windmill graph, 13G05

References

I. Beck .1988 .. J. Algebra, 116(1) : 208-226.

Coyekendall J.,Maney J. .2007 .Irreducible divisor graphs. Comm. Algebra, 35 : 885-895.

McAdam S.,Swan R.G. .2004 .. J. Algebra, 276 : 180-192.

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