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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)
  • Received : 2020.07.03
  • Accepted : 2020.12.09
  • Published : 2021.07.31

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

References

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