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arXiv · 1705.09799

Factorizations in Modules and Splitting Multiplicatively Closed Subsets

Ashkan Nikseresht
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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.

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BibTeXRIS

Ashkan Nikseresht. 2017-05-27. Factorizations in Modules and Splitting Multiplicatively Closed Subsets. https://doi.org/10.4134/jkms.j160810

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