On weakly 2-absorbing δ-primary ideals of commutative rings
Let R be a commutative ring with 1≠ 0. We recall that a proper ideal I of R is called a weakly
2-absorbing primary ideal of R if whenever a, b, c∈ R and 0≠ a b c∈ I, then a b∈ I or
a c∈ I or b c∈ I. In this paper, we introduce a new class of ideals that is closely related to
the class of weakly 2-absorbing primary ideals. Let I(R) be the set of all ideals of R and let
δ: I(R)→ I(R) be a function. Then δ is called an expansion function of ideals of R if
whenever L, I, J are ideals of R with J⊆ I, then L⊆ δ(L) and δ(J)⊆ δ(I). Let δ be an …
2-absorbing primary ideal of R if whenever a, b, c∈ R and 0≠ a b c∈ I, then a b∈ I or
a c∈ I or b c∈ I. In this paper, we introduce a new class of ideals that is closely related to
the class of weakly 2-absorbing primary ideals. Let I(R) be the set of all ideals of R and let
δ: I(R)→ I(R) be a function. Then δ is called an expansion function of ideals of R if
whenever L, I, J are ideals of R with J⊆ I, then L⊆ δ(L) and δ(J)⊆ δ(I). Let δ be an …
Abstract
Let R be a commutative ring with . We recall that a proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever and , then or or . In this paper, we introduce a new class of ideals that is closely related to the class of weakly 2-absorbing primary ideals. Let be the set of all ideals of R and let be a function. Then δ is called an expansion function of ideals of R if whenever are ideals of R with , then and . Let δ be an expansion function of ideals of R. Then a proper ideal I of R (i.e., ) is called a weakly 2-absorbing δ-primary ideal if implies or or . For example, let such that . Then δ is an expansion function of ideals of R, and hence a proper ideal I of R is a weakly 2-absorbing primary ideal of R if and only if I is a weakly 2-absorbing δ-primary ideal of R. A number of results concerning weakly 2-absorbing δ-primary ideals and examples of weakly 2-absorbing δ-primary ideals are given.
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