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Proceedings of the Yerevan State University, series Physical and Mathematical Sciences, 2023, Volume 57, Issue 1, Pages 9–22
DOI: https://doi.org/10.46991/PYSU:A/2023.57.1.009 (Mi uzeru1034) 		 
Mathematics

Linearity of $n$-ary associative algebras

D. N. Harutyunyan

Yerevan State University, Faculty of Mathematics and Mechanics
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DOI: https://doi.org/10.46991/PYSU:A/2023.57.1.009
Abstract: In this paper $n$-ary regular division associative algebras are discussed. It is shown that every operation in $n$-ary regular division associative algebra will be endo-linearly represented over the same binary group. Schaufler like theorem will be proved for those algebras.
Keywords: $\forall\exists(\forall)$-identities, regular division groupoids, $n$-ary groupoids, quasiendomorphisms, Schaufler theorem.
Received: 17.02.2023
Revised: 04.05.2023
Accepted: 17.05.2023
Document Type: Article
MSC: Primary 03C05; Secondary 03C85, 20N05
Language: English
Citation: D. N. Harutyunyan, “Linearity of $n$-ary associative algebras”, Proceedings of the YSU, Physical and Mathematical Sciences, 57:1 (2023), 9–22
Citation in format AMSBIB
\Bibitem{Har23}
\by D.~N.~Harutyunyan
\paper Linearity of $n$-ary associative algebras
\jour Proceedings of the YSU, Physical and Mathematical Sciences
\yr 2023
\vol 57
\issue 1
\pages 9--22
\mathnet{http://mi.mathnet.ru/uzeru1034}
\crossref{https://doi.org/10.46991/PYSU:A/2023.57.1.009}
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