A corrigendum to “Hereditary properties between a ring and its maximal subrings” - Gaur, A.; Kumar, R. (Ukrains’kyi Matematychnyi Zhurnal, 2018)
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 $dim(S) = 1$ implies that $dim(R) = 1$ if and only if$(S : R) = 0$. An example is given which shows the above mentioned proposition is not correct.