2021/02/14 by Khalfi, Abdelhaq El, Mahdou, Najib, Tekir, Ünsal +1
#13A99 #13C13 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2102.07189
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)\longrightarrow 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.