Rings in which every ideal contained in the set of zero-divisors is a d-ideal
Commun. Korean Math. Soc. 2022 Vol. 37, No. 1, 45-56
Published online July 8, 2021
Printed January 31, 2022
Adam Anebri, Najib Mahdou, Abdeslam Mimouni
University S.M. Ben Abdellah Fez; University S.M. Ben Abdellah Fez; King Fahd University of Petroleum \& Minerals
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, d$_E$-ideal
MSC numbers : Primary 13B99; Secondary 13A15, 13G05, 13B21
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