A Corrigendum to “Hereditary Properties Between a Ring and Its Maximal Subrings”

Abstract

Let R be a commutative ring with identity. In A. Azarang, O. A. S. Karamzadeh, and A. Namazi, [Ukr. Math. J., 65, No. 7, 981–994 (2013) (Proposition 3.1)], it was proved that if R is an integral domain and S is a maximal subring of R 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 that the above-mentioned proposition is not true.