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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