Erratum to ``Rings in which every ideal contained in the set of zero-divisors is a d-ideal

Adam Anebri; Najib Mahdou; Abdeslam Mimouni

doi:10.4134/CKMS.c220054

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2023; 38(1): 121-122

Online first article December 6, 2022 Printed January 31, 2023

https://doi.org/10.4134/CKMS.c220054

Erratum to ``Rings in which every ideal contained in the set of zero-divisors is a d-ideal", Commun. Korean Math. Soc. 37 (2022), No. 1, pp. 45--56

Adam Anebri, Najib Mahdou, Abdeslam Mimouni

Box 2202, University S.M. Ben Abdellah Fez; Box 2202, University S.M. Ben Abdellah Fez; King Fahd University of Petroleum \& Minerals

Abstract

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Abstract

In this erratum, we correct a mistake in the proof of Proposition 2.7. In fact the equivalence $(3)\Longleftarrow (4)$ ``$R$ is a quasi-regular ring if and only if $R$ is a reduced ring and every principal ideal contained in $Z(R)$ is a 0-ideal'' does not hold as we only have $Rx\subseteq O(S)$.

Keywords: AA-ring, d-ideal

MSC numbers: Primary 13B99; Secondary 13A15, 13G05, 13B21