Authors: Ehsani, Amir
Krapež, Aleksandar 
Movsisyan, Yuri
Title: Algebras with parastrophically uncancellable quasigroup equations
Journal: Buletinul Academiei de Stiinte a Republicii Moldova. Matematica
Volume: 80
Issue: 1
First page: 41
Last page: 63
Issue Date: 1-Jan-2016
ISSN: 1024-7696
Abstract: 
We consider 48 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 obtained.
Keywords: Algebra of quasigroup operations | Balanced equation | Belousov equation | Gemini equation | Hyperidentity | Level equation | Medial–like equation | Parastrophically uncancellable equation | Quadratic equation | Quasigroup operation
Publisher: Academia de Stiinte a Moldovej
Project: Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security 
Representations of logical structures and formal languages and their application in computing 

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