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Algebras with Parastrophically Uncancellable Quasigroup Equations
Authors: Amir Ehsani, Aleksandar Krapež, Yuri Movsisyan
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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.Amir Ehsani
Department of Mathematics, Mahshahr Branch
Islamic Azad University, Mahshahr, Iran
E-mail: Aleksandar Krapež
Mathematical Institute of the Serbian Academy
of Sciences and Arts, Knez Mihailova 36
11001 Belgrade, Serbia
E-mail: Yuri Movsisyan
Department of Mathematics and Mechanics
Yerevan State University, Alex Manoogian 1
Yerevan 0025, Armenia.
E-mail:
Department of Mathematics, Mahshahr Branch
Islamic Azad University, Mahshahr, Iran
E-mail: Aleksandar Krapež
Mathematical Institute of the Serbian Academy
of Sciences and Arts, Knez Mihailova 36
11001 Belgrade, Serbia
E-mail: Yuri Movsisyan
Department of Mathematics and Mechanics
Yerevan State University, Alex Manoogian 1
Yerevan 0025, Armenia.
E-mail:
Fulltext
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Contents
- Valentin Belousov (20.02.1925 - 23.07.1988)
- Belousov's Theorem and the quantum Yang-Baxter equation
- Central and medial quasigroups of small order
- Algebras with Parastrophically Uncancellable Quasigroup Equations
- Linear groups that are the multiplicative groups of neofields
- On isotopies of some classes of Moufang loops
- Doubly transitive sets of even permutations
- Triality and Universal Multiplication Groups of Moufang Loops
- On paratopies of orthogonal systems of ternary quasigroups. I
- On cosets in Steiner loops
