2019
Том 71
№ 8

All Issues

Kumar R.

Articles: 2
Brief Communications (English)

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

Gaur A., Kumar R.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 4. - pp. 583-584

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.

Article (Ukrainian)

Slant lightlike submersions from an indefinite almost Hermitian manifold onto a lightlike manifold

Bhatia S. S., Kumar R., Sachdeva R.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 963-971

We introduce slant lightlike submersions from an indefinite almost Hermitian manifold onto a lightlike manifold. We establish existence theorems for these submersions. We also investigate the necessary and sufficient conditions for the leaves of the distributions to be totally geodesic foliations in indefinite almost Hermitian manifolds.