Abstract
A commutative ring R is said to satisfy acc on d-annihilators if for every sequence [Formula: see text] of elements of R, the sequence [Formula: see text] is stationary. In this paper we extend the notion of rings with acc on d-annihilators by introducing the concept of rings with S-acc on d-annihilators, where S is a multiplicative set. Let R be a commutative ring and S a multiplicative subset of R. We say that R satisfies S-acc on d-annihilators if for every sequence [Formula: see text] of elements of R, the sequence [Formula: see text] is S-stationary, that is, there exist a positive integer n and an [Formula: see text] such that for each [Formula: see text], [Formula: see text]. We give equivalent conditions for the power series (respectively, polynomial) ring over an Armendariz ring to satisfy S-acc on d-annihilators. We also study serval properties of rings satisfying S-acc on d-annihilators. The concept of the amalgamated duplication of R along an ideal I, [Formula: see text] is studied.
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