Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica, cilt.29, sa.3, ss.1-16, 2021 (SCI-Expanded)
Let R be a commutative ring with nonzero identity. 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, we have L ⊆ δ(L) and δ(J) ⊆ δ(I). Let δ
be an expansion function of ideals of R. In this paper, we introduce
and investigate a new class of ideals that is closely related to the class
of δ-primary ideals. A proper ideal I of R is said to be a 1-absorbing
δ-primary ideal if whenever nonunit elements a, b, c ∈ R and abc ∈ I,
then ab ∈ I or c ∈ δ(I). Moreover, we give some basic properties of
this class of ideals and we study the 1-absorbing δ-primary ideals of
the localization of rings, the direct product of rings and the trivial ring
extensions.