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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2018; 55(1): 83-99

Online first article August 2, 2017      Printed January 1, 2018

https://doi.org/10.4134/JKMS.j160810

Copyright © The Korean Mathematical Society.

Factorization in modules and splitting multiplicatively closed subsets

Ashkan Nikseresht

Institute for Advanced Studies in Basic Sciences

Abstract

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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

MSC numbers: 13A05, 13F15, 13C99

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