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This article is cited in 7 scientific papers (total in 7 papers)
Series of articles on the multioperator rings and algebras
Two theorems on identities in multioperator algebras
F. I. Kizner
Abstract:
Two (unconnected) propositions on $\Omega$-algebras with identical relations are proved. The first of these (Theorem 1, in § 1) generalizes to $\Omega$-algebras a known fact from the theory of associative linear algebras, which asserts that every finite-dimensional algebra is an algebra with identical relations (more exactly, every algebra $A$ of dimension over a field $m$ satisfies a so-called standard identity of degree $m+1$).
In § 2 we prove that every identical relation in an $\Omega$-algebra over a field of characteristic zero is equivalent to a system of polylinear identical relations (Theorem 2), from which it follows that the study of $\Omega$-algebras with arbitrary identical relations reduces to that of $\Omega$-algebras with polylinear identical relations. This theorem is proved in practically the same way as the corresponding proposition for ordinary algebras with identical relations, that is, algebras with a single binary multiplication (see for example, Mal'tsev [1]); it is clearly a generalization of it.
Received: 30.09.1968
Citation:
F. I. Kizner, “Two theorems on identities in multioperator algebras”, Uspekhi Mat. Nauk, 24:1(145) (1969), 39–42; Russian Math. Surveys, 24:1 (1969), 37–40
Linking options:
https://www.mathnet.ru/eng/rm5449https://doi.org/10.1070/RM1969v024n01ABEH001337 https://www.mathnet.ru/eng/rm/v24/i1/p39
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Abstract page: | 262 | Russian version PDF: | 99 | English version PDF: | 4 | References: | 53 | First page: | 1 |
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