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ЖУРНАЛЫ // Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica // Архив

Bul. Acad. Ştiinţe Repub. Mold. Mat., 2016, номер 1, страницы 41–63 (Mi basm413)

Эта публикация цитируется в 4 статьях

Algebras with parastrophically uncancellable quasigroup equations

Amir Ehsania, Aleksandar Krapežb, Yuri Movsisyanc

a Department of Mathematics, Mahshahr Branch, Islamic Azad University, Mahshahr, Iran
b Mathematical Institute of the Serbian Academy of Sciences and Arts, Knez Mihailova 36, 11001 Belgrade, Serbia
c Department of Mathematics and Mechanics, Yerevan State University, Alex Manoogian 1, Yerevan 0025, Armenia

Аннотация: 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.

Ключевые слова и фразы: quadratic equation, gemini equation, level equation, balanced equation, Belousov equation, medial-like equation, parastrophically uncancellable equation, quasigroup operation, algebra of quasigroup operations, hyperidentity.

MSC: 20N05, 39B52, 08A05

Поступила в редакцию: 20.11.2015

Язык публикации: английский



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