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 ...

Let R be a commutative ring with non-zero identity and M be a unitary R-module. The goal of this paper is to extend the concept of 1-absorbing primary ideals to 1-absorbing primary submodules. A proper submodule N of M is ...

Let R be a commutative ring with 1 not equal 0. We introduce the concept of weakly 1-absorbing primary ideal, which is a generalization of 1-absorbing primary ideal. A proper ideal I of R is said to be weakly 1-absorbing ...