Algebras with Parastrophically Uncancellable Quasigroup Equations

Ehsani Amir; Krapez Aleksandar; Movsisyan Yuri

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2018-02-26 13:28

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512.5 (335)

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SM ISO690:2012

EHSANI, Amir, KRAPEZ, Aleksandar, MOVSISYAN, Yuri. Algebras with Parastrophically Uncancellable Quasigroup Equations. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2016, nr. 1(80), pp. 41-63. ISSN 1024-7696.

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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica

Numărul 1(80) / 2016 / ISSN 1024-7696 /ISSNe 2587-4322

Algebras with Parastrophically Uncancellable Quasigroup Equations

CZU: 512.5

Pag. 41-63

Ehsani Amir¹, Krapez Aleksandar², Movsisyan Yuri³

¹ Islamic Azad University, Mahshahr,
² Mathematical Institute of the Serbian Academy of Sciences and Arts,
³ Yerevan State University

Disponibil în IBN: 19 iulie 2016

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Rezumat

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.

Cuvinte-cheie
Quadratic equation, Gemini equation, Level equation, Balanced equation, Belousov equation, Medial–like equation, Parastrophically uncancellable equation, Quasigroup operation, Algebra of quasigroup operations, Hyperidentity

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