DSpace Collection:
http://hdl.handle.net/123456789/4383
2024-03-29T11:56:09ZPlanarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case
http://hdl.handle.net/123456789/4545
Title: Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case
Authors: Vadhel, P.; Visweswaran, S.
Abstract: 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.
Description: 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.130-1432018-01-01T00:00:00ZOn the anticommutativity in Leibniz algebras
http://hdl.handle.net/123456789/4544
Title: On the anticommutativity in Leibniz algebras
Authors: Kurdachenko, L.; Semko, N.; Subbotin, I.
Abstract: 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).
Description: Kurdachenko L. On the anticommutativity in Leibniz algebras / L.Kurdachenko , N. Semko , I. Subbotin // Algebra and Discrete Mathematics. - 2018. - Vol. 26. - Number 1. - Рp. 97-1092018-01-01T00:00:00ZOn finite groups with Hall normally embedded Schmidt subgroups
http://hdl.handle.net/123456789/4543
Title: On finite groups with Hall normally embedded Schmidt subgroups
Authors: Kniahina, V. N.; Monakhov, V. S.
Abstract: 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.
Description: 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. 90-962018-01-01T00:00:00ZType conditions of stable range for identification of qualitative generalized classes of rings
http://hdl.handle.net/123456789/4541
Title: Type conditions of stable range for identification of qualitative generalized classes of rings
Authors: Zabavsky, B.
Abstract: 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.
Description: 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- 1522018-01-01T00:00:00Z