HOLOMORPH OF GENERALIZED BOL LOOPS II
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2015, Vol 35, Issue 1
Abstract
The notion of the holomorph of a generalized Bol loop (GBL) is characterized afresh. The holomorph of a right inverse property loop (RIPL) is shown to be a GBL if and only if the loop is a GBL and some bijections of the loop are right (middle) regular. The holomorph of a RIPL is shown to be a GBL if and only if the loop is a GBL and some elements of the loop are right (middle) nuclear. Necessary and sufficient conditions for the holomorph of a RIPL to be a Bol loop are deduced. Some algebraic properties and commutative diagrams are established for a RIPL whose holomorph is a GBL.
Authors and Affiliations
Temıtope Gbolahan Jaıyeola, Bolaji Ajibola Popoola
Keywords
Related Articles
- EP ID EP304461
- DOI -
- Views 44
- Downloads 0
CONRAD’S PARTIAL ORDER ON P.Q.-BAER ∗-RINGS
We prove that a p.q.-Baer ∗-ring forms a pseudo lattice with Conrad’s partial order and also characterize p.q.-Baer ∗-rings which are lattices. The initial segments of a p.q.-Baer ∗-ring with the Conrad’s partial order a...
Jordan numbers, Stirling numbers and sums of powers
In the paper a new combinatorical interpretation of the Jordan numbers is presented. Binomial type formulae connecting both kinds of numbers mentioned in the title are given. The decomposition of the product of polynomia...
NONDISTRIBUTIVE RINGS AND THEIR ORE ¨ LOCALIZATIONS
In the paper, we introduce the notion of a nondistributive ring N as a generalization of the notion of an associative ring with unit, in which the addition needs not be abelian and the distributive law is replaced by n0...
Note on Ideal Based Zero-Divisor Graph of a Commutative Ring
In this paper, we consider the ideal based zero divisor graph I (R) of a commutative ring R. We discuss some graph theoretical properties of I (R) in relation with zero divisor graph. We also relate certain parameters...
NON-DETERMINISTIC LINEAR HYPERSUBSTITUTIONS
A non-deterministic hypersubstitution maps operation symbols to sets of terms of the corresponding arity. A non-deterministic hypersubstitution of type τ is said to be linear if it maps any operation symbol to a set of l...