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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