A study of linked star operations

摘要

Abstract. Let R ? L ? S be ring extensions. Two star operations ∈ Star(R, S), ∈ Star(L, S) are said to be linked if whenever for some finitely generated S-regular R-submodule A of S, then . We study properties of linked star operations; especially when are strict star operations. We introduce the notion of Pr¨ufer star multiplication extension and we show that under appropriate conditions, if the extension R ? S is and is linked to , then L ? S is .