A corrigendum to “Hereditary properties between a ring and its maximal subrings”

  • A. Gaur
  • R. Kumar


Let $R$ be a commutative ring with identity. In [2] (Proposition 3.1), Azarang proved that if $R$ is an integral domain and $S$ is a maximal subring of $R$, and is integrally closed in $R$, then $\mathrm{d}\mathrm{i}\mathrm{m}(S) = 1$ implies that $\mathrm{d}\mathrm{i}\mathrm{m}(R) = 1$ if and only if $(S : R) = 0$. An example is given which shows the above mentioned proposition is not correct.
How to Cite
Gaur, A., and R. Kumar. “A Corrigendum to ‘Hereditary Properties Between a Ring and Its Maximal subrings’”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, no. 4, Apr. 2018, pp. 583-4, http://umj.imath.kiev.ua/index.php/umj/article/view/1578.
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