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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2018, Number 2, Pages 95–100
(Mi basm474)
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This article is cited in 1 scientific paper (total in 1 paper)
Research articles
General method for defining finite non-commutative associative algebras of dimension $m>1$
A. A. Moldovyan St. Petersburg Institute for Informatics and Automation of Russian Academy of Sciences, 14-th line 39, 199178, St. Petersburg, Russia
Abstract:
General method for defining non-commutative finite associative algebras of arbitrary dimension $m\ge2$ is discussed. General formulas describing local unit elements (the right-, left-, and bi-side ones), square roots of zero and zero divisors are derived. For arbitrary value $m$ the single bi-side unit corresponds to every element of the algebra, except the square roots from zero. Various modifications of the multiplication operation can be assigned using different sets of the values of structural coefficients. It is proved that all of the modifications are mutually associative.
Keywords and phrases:
finite associative algebra, non-commutative algebra, structural coefficient, mutual associativity, local unit.
Received: 02.05.2018
Citation:
A. A. Moldovyan, “General method for defining finite non-commutative associative algebras of dimension $m>1$”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2018, no. 2, 95–100
Linking options:
https://www.mathnet.ru/eng/basm474 https://www.mathnet.ru/eng/basm/y2018/i2/p95
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Abstract page: | 179 | Full-text PDF : | 35 | References: | 18 |
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