arXiv subjects

A. O. Abdulkareem

Publications and source records attributed to A. O. Abdulkareem.

5 recordsLinked to original sources

arXiv2019

Universal $α$-elasticity of generalized Moufang loops

In this study we introduce $α$-elasticity property for generalized Moufang loops. Necessary and sufficient conditions for $α$-elasticity of generalized Moufang loops to be universal are given. Using the universal conditions, and in some cases, with the newly introduced right and left $α$-alternative laws for generalized Moufang loops, some properties of generalized Moufang loops are studied. Condition under which the generalized Moufang loop is an abelian group is stated.

math.GR↗

arXiv2017

Rigidity of some classes of Lie algebras in connection to Leibniz algebras

In this paper we focus on algebraic aspects of contractions of Lie and Leibniz algebras. The rigidity of algebras plays an important role in the study of their varieties. The rigid algebras generate the irreducible components of this variety. We deal with Leibniz algebras which are generalizations of Lie algebras. In Lie algebras case, there are different kind of rigidities (rigidity, absolutely rigidity, geometric rigidity and e.c.t.). We explore the relations of these rigidities with Leibniz algebra rigidity. Necessary conditions for a Lie algebra to be Leibniz rigid are discussed.

math.RA↗

arXiv2017

On generalization of Rad-$D_{11}$-module

This paper gives generalization of a notion of supplemented module. Here, we utilize some algebraic properties like supplemented, amply supplemented and local modules in order to obtain the generalization. Other properties that are instrumental in this generalization are $D_{i}$, $SSP$ and $SIP$. If a module $M$ is $Rad$-$D_{11}$-module and has $D_{3}$ property, then $M$ is said to be completely-$Rad$-$D_{11}$-module ($C$-$Rad$-$D_{11}$-module). Similarly it is for $M$ with $SSP$ property. We provide some conditions for a supplemented module to be $C$-$Rad$-$D_{11}$-module.

math.RA↗

arXiv2016

Derivations and Centroids of Four Dimensional Associative Algebras

In this paper, we focus on derivations and centroids of four dimensional associative algebras. Using an existing classification result of low dimensional associative algebras, we describe the derivations and centroids of four dimensional associative algebras. We also identify algebra(s) that belong to the characteristically nilpotent class among the algebras of four dimensional associative algebras.

math.RA↗

arXiv2013

Isomorphism classes and invariants of low dimensional filiform Leibniz algebras

In this study, we extend the result on classification of a subclass of filiform Leibniz algebras in low dimensions to dimensions seven and eight based on the technique used by Rakhimov and Bekbaev for classification of subclasses which arise from naturally graded non-Lie filiform Leibniz algebras. The subclass considered here arises from naturally graded filiform Lie algebras. This subclass contains the class of filiform Lie algebras and consequently, by classifying this subclass, we again re-examine the classification of filiform Lie algebras. Our resulting list of filifom Lie algebras is compared with that given by Ancochéa-Bermudez and Goze in 1988 and by Gómez, Jimenez-Merchan and Khakimdjanov in 1998.

math.RA↗