On S-valuation domains

Dong Kyu Kim; Jung Wook Lim

doi:10.1142/S0219498825501920

On S-valuation domains

Dong Kyu Kim, Jung Wook Lim

Kyungpook National University

Research output: Contribution to journal › Article › peer-review

Abstract

Let D be an integral domain and let S be a multiplicative subset of D. In this paper, we study integral domains whose quotient rings are valuation domain. To do this, we introduce the concept of S-valuation domains. We define D to be an S-valuation domain if for each nonzero a, b ∈ D, there exists an element s ∈ S such that a divides sb or b divides sa. Among other things, we show that D is an S-valuation domain if and only if D_S is a valuation domain. By using this result, we give several valuation-like properties.

Original language	English
Article number	2550192
Journal	Journal of Algebra and its Applications
DOIs	https://doi.org/10.1142/S0219498825501920
State	Accepted/In press - 2024

Keywords

maximal S-valuation overring
minimal S-valuation overring
Prüfer ∗-multiplication domain
S-valuation domain
valuation domain

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10.1142/S0219498825501920

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On S-valuation domains

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Keywords

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