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http://dx.doi.org/10.4134/JKMS.j160810

FACTORIZATION IN MODULES AND SPLITTING MULTIPLICATIVELY CLOSED SUBSETS  

Nikseresht, Ashkan (Department of Mathematics Institute for Advanced Studies in Basic Sciences)
Publication Information
Journal of the Korean Mathematical Society / v.55, no.1, 2018 , pp. 83-99 More about this Journal
Abstract
We introduce the concept of multiplicatively closed subsets of a commutative ring R which split an R-module M and study factorization properties of elements of M with respect to such a set. Also we demonstrate how one can utilize this concept to investigate factorization properties of R and deduce some Nagata type theorems relating factorization properties of R to those of its localizations, when R is an integral domain.
Keywords
splitting multiplicatively closed subset; factorization; atomicity;
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