Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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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 (Laboratory of Modelling and Mathematical Structures Department of Mathematics Faculty of Science and Technology of Fez) ;
  • Najib Mahdou (Laboratory of Modelling and Mathematical Structures Department of Mathematics Faculty of Science and Technology of Fez) ;
  • Abdeslam Mimouni (Department of Mathematics and Statistics King Fahd University of Petroleum & Minerals)
  • Received : 2022.02.25
  • Accepted : 2022.05.16
  • Published : 2023.01.31
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Abstract

In this erratum, we correct a mistake in the proof of Proposition 2.7. In fact the equivalence (3) ⇐ (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 ⊆ O(S).

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References

  1. A. Anebri, N. Mahdou, and A. Mimouni, Rings in which every ideal contained in the set of zero-divisors is a d-ideal, Commun. Korean Math. Soc. 37 (2022), no. 1, 45-56. https://doi.org/10.4134/CKMS.c200467