Abstract
The following Artin theorem about alternative linear algebras defined on the commutative, associative ring with unity is well-known: in an alternative linear algebra, if \((a,b,c)=0\), then the subalgebra generated by the elements \(a\), \(b\), and \(c\) is associative. In this paper a wide generalization of this classical result is proposed using the concepts of hyperidentity and coidentity. The corresponding universal algebras are referred to as \(g\)-algebras.
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The work is partially supported by the State Committee of the Republic of Armenia, projects nos. 10-3/1-41 and 21T-1A213.
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Translated by E. Oborin
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Movsisyan, Y.M., Yolchyan, M.A. A Generalization of the Artin Theorem. J. Contemp. Mathemat. Anal. 56, 104–111 (2021). https://doi.org/10.3103/S1068362321020060
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DOI: https://doi.org/10.3103/S1068362321020060