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Factorization in modules and splitting multiplicatively closed subsets

Ashkan Nikseresht
대한수학회 (The Korean Mathematical Society)|2018.01|대한수학회지 (Journal of the KMS)|제55권 제1호|pp. 83-99

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키워드

atomicityfactorizationsplitting multiplicatively closed subset
주제분류수학

초록

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.

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.

참고문헌 (20)

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관련 논문AI추천

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