A study of linked star operations

Document Type

Article

Publication Date

1-1-2021

Publication Title

Bulletin of the Korean Mathematical Society

Abstract

Let R ⊆ L ⊆ S be ring extensions. Two star operations ⋆1 ∈ Star(R, S), ⋆2 ∈Star(L, S) are said to be linked if whenever A⋆1 = R⋆1 for some finitely generated S-regular R-submodule A of S, then (AL)⋆2 = L⋆2. We study properties of linked star operations; especially when ⋆1 and ⋆2 are strict star operations. We introduce the notion of Prüfer star multiplication extension (P⋆ME) and we show that under appropriate conditions, if the extension R ⊆ S is P⋆1ME and ⋆1 is linked to ⋆2, then L ⊆ S is P⋆2ME.

Department

Mathematics

Volume Number

58

Issue Number

4

First Page

837

Last Page

851

DOI

10.4134/BKMS.b200576

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