Generalizations of 1-absorbing primary ideals of commutative rings

Abstract

Let R be a commutative ring with identity. In this paper, we extend the concept of 1-absorbing primary ideals to the concept of ֆ-1-absorbing primary ideals. Let ֆ: S(R) → S(R) ∪ {∅} be a function, where S(R) is the set of all ideals of R. A proper ideal Ī of R is called a ֆ-1-absorbing primary ideal of R if whenever nonunit elements a, b, c of R and abc ∈ Ī\ֆ(Ī), then ab ∈ Ī or c ∈ √Ī. A number of results concerning ֆ-1-absorbing primary ideals are given and some characterizations of ֆ-1-absorbing primary ideals in some special rings are obtained. © 2020, Politechnica University of Bucharest. All rights reserved.