[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b200576

A STUDY OF LINKED STAR OPERATIONS

Paudel, Lokendra (Department of Mathematics University of South Carolina-Salkehatchie)
Tchamna, Simplice (Department of Mathematics Georgia College & State University)

Publication Information

Bulletin of the Korean Mathematical Society / v.58, no.4, 2021 , pp. 837-851 More about this Journal

Abstract

Let R ⊆ L ⊆ S be ring extensions. Two star operations ${\ast}_1{\in}Star(R,S)$ , ${\ast}_2{\in}Star(L,S)$ are said to be linked if whenever $A^{{\ast}_1}= R^{{\ast}_1}$ for some finitely generated S-regular R-submodule A of S, then $(AL)^{{\ast}_2}=L^{{\ast}_2}$ . We study properties of linked star operations; especially when ${\ast}_1$ and ${\ast}_2$ are strict star operations. We introduce the notion of Prüfer star multiplication extension ( $P{\ast}ME$ ) and we show that under appropriate conditions, if the extension R ⊆ S is $P{\ast}_1ME$ and ${\ast}_1$ is linked to ${\ast}_2$ , then L ⊆ S is $P{\ast}_2ME$ .

Keywords

Star operation; ring extension; localization; $Pr{\ddot{u}}fer$ extension;

Citations & Related Records

Reference

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