Let R be a commutative ring with {1\neq 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\in R} and {0\not=abc\in I} , then {ab\in I} or {ac\in\sqrt{I}} or {bc\in\sqrt{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 {\delta:I(R)\rightarrow 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\subseteq I} , then {L\subseteq\delta(L)} and {\delta(J)\subseteq\delta(I)} . Let δ be an expansion function of ideals of R. Then a proper ideal I of R (i.e., {I\not=R} ) is called a weakly 2-absorbing δ-primary ideal if {0\not=abc\in I} implies {ab\in I} or {ac\in\delta(I)} or {bc\in\delta(I)} . For example, let {\delta:I(R)\rightarrow I(R)} such that {\delta(I)=\sqrt{I}} . 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.

The notion of trivial extension of a ring by a module has been extensively studied 2010 Mathematics Subject Classification. primary 13A02, 13A05, 13A15, 13B99, 13E05, 13F05, 13F30; secondary 16S99, 17A99.

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