τ -U-FACTORIZATIONS AND THEIR GRAPHS IN COMMUTATIVE RINGS WITH ZERO-DIVISORS

Authors : M Axtell, C Mooney

Pages : 72-91

Doi:10.24330/ieja.266205

View : 19 | Download : 12

Publication Date : 2015-12-01

Article Type : Research Paper

Abstract :Let R be a commutative ring with identity, and let τ be a relation on the nonzero, non-unit elements of R. In this paper we generalize the defi- nitions of a factorization and a U-factorization via a relation τ and construct a variety of graphs based on these generalizations. These graphs are then examined in an effort to determine ring-theoretic properties.
Keywords : Commutative ring, irreducible, U factorization, τ factorization, graph