http://hdl.handle.net/123456789/4383 2026-04-15T22:53:04Z 2026-04-15T22:53:04Z Vadhel, P. Visweswaran, S. http://hdl.handle.net/123456789/4545 2020-01-08T15:07:12Z 2018-01-01T00:00:00Z

Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case Vadhel, P.; Visweswaran, S. The rings considered in this article are nonzero commutative with identity which are not fields. Let R be a ring. We denote the collection of all proper ideals of R by I(R) and the collection I(R)\{(0)} by I(R) ∗ . Recall that the intersection graph of ideals of R, denoted by G(R), is an undirected graph whose vertex set is I(R) ∗ and distinct vertices I, J are adjacent if and only if I ∩J = (0) 6 . In this article, we consider a subgraph of G(R), denoted by H(R), whose vertex set is I(R) ∗ and distinct vertices I, J are adjacent in H(R) if and only if IJ 6= (0). The purpose of this article is to characterize rings R with at least two maximal ideals such that H(R) is planar. Vadhel P. Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case / P. Vadhel , S. Visweswaran // Algebra and Discrete Mathematics. - 2018. - Vol. 26. - Number 1. - Рp.130-143

2018-01-01T00:00:00Z Kurdachenko, L. Semko, N. Subbotin, I. http://hdl.handle.net/123456789/4544 2020-01-08T15:07:12Z 2018-01-01T00:00:00Z

On the anticommutativity in Leibniz algebras Kurdachenko, L.; Semko, N.; Subbotin, I. Lie algebras are exactly the anticommutative Leibniz algebras. In this article, we conduct a brief analysis of the approach to Leibniz algebras which based on the concept of the anti-center (Lie-center) and antinilpotency (Lie nilpotentency). Kurdachenko L. On the anticommutativity in Leibniz algebras / L.Kurdachenko , N. Semko , I. Subbotin // Algebra and Discrete Mathematics. - 2018. - Vol. 26. - Number 1. - Рp. 97-109

2018-01-01T00:00:00Z Kniahina, V. N. Monakhov, V. S. http://hdl.handle.net/123456789/4543 2020-01-08T15:07:11Z 2018-01-01T00:00:00Z

On finite groups with Hall normally embedded Schmidt subgroups Kniahina, V. N.; Monakhov, V. S. A subgroup H of a finite group G is said to be Hall normally embedded in G if there is a normal subgroup N of G such that H is a Hall subgroup of N. A Schmidt group is a non-nilpotent finite group whose all proper subgroups are nilpotent. In this paper, we prove that if each Schmidt subgroup of a finite group G is Hall normally embedded in G, then the derived subgroup of G is nilpotent. Kniahina V. N. On finite groups with Hall normally embedded Schmidt subgroups / V. N. Kniahina , V. S. Monakhov // Algebra and Discrete Mathematics. - 2018. - Vol. 26. - Number 1. - Рp. 90-96

2018-01-01T00:00:00Z Zabavsky, B. http://hdl.handle.net/123456789/4541 2020-01-08T15:07:11Z 2018-01-01T00:00:00Z

Type conditions of stable range for identification of qualitative generalized classes of rings Zabavsky, B. This article deals mostly with the following question: when the classical ring of quotients of a commutative ring is a ring of stable range 1? We introduce the concepts of a ring of (von Neumann) regular range 1, a ring of semihereditary range 1, a ring of regular range 1, a semihereditary local ring, a regular local ring. We find relationships between the introduced classes of rings and known ones, in particular, it is established that a commutative indecomposable almost clean ring is a regular local ring. Any commutative ring of idempotent regular range 1 is an almost clean ring. It is shown that any commutative indecomposable almost clean Bezout ring is an Hermite ring, any commutative semihereditary ring is a ring of idempotent regular range 1. The classical ring of quotients of a commutative Bezout ring QCl(R) is a (von Neumann) regular local ring if and only if R is a commutative semihereditary local ring. Zabavsky B. Type conditions of stable range for identification of qualitative generalized classes of rings / B. Zabavsky // Algebra and Discrete Mathematics. - 2018. - Vol. 26. - Number 1. - Рp. 144- 152

2018-01-01T00:00:00Z