Algebras with Parastrophically Uncancellable Quasigroup Equations
Group Theory
2016-01-11 v1
Abstract
We consider parastrophically uncancellable quadratic functional equations with four object variables and two quasigroup operations in two classes: balanced non--Belousov (consists of 16 equations) and non--balanced non--gemini (consists of 32 equations). A linear representation of a group (Abelian group) for a pair of quasigroup operations satisfying one of these parastrophically uncancellable quadratic equations is obtained. As a consequence of these results, a linear representation for every operation of a binary algebra satisfying one of these hyperidentities is presented.
Cite
@article{arxiv.1601.01922,
title = {Algebras with Parastrophically Uncancellable Quasigroup Equations},
author = {Amir Ehsani and Aleksandar Krapež and Yuri Movsisyan},
journal= {arXiv preprint arXiv:1601.01922},
year = {2016}
}
Comments
23 pages, 2 figures, submitted to Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica