Rings in which every ideal contained in the set of zero-divisors is a d-ideal
Commun. Korean Math. Soc. Published online July 8, 2021
A Anebri, N. Mahdou, and A. Mimouni
University of Fez, Morocco; University of Fez, Morocco; KFUPM, KSA
Abstract : In this paper, we introduce and study the class of rings in which every ideal consisting entirely of zero divisors is a d-ideal, considered as a generalization of strongly duo rings. Some results including the characterization of AA-rings are given in the first section. Further, we examine the stability of these rings in localization and study the possible transfer to direct product and trivial ring extension. In addition, we define the class of d_E-ideals which allows us to characterize von Neumann regular rings.
Keywords : AA-ring, strongly duo ring, trivial ring extension, localization, direct product, d-ideal, dE-ideal.