On Mixed Identities of Endomorphs, Bimodules, and $ \omega $-Algebras Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2025, Volume: 66, Number: 4, Pages: 1031-1042 Pages count : 12 DOI: 10.1134/s0037446625040135 | ||
| Tags | endomorph, right-symmetric algebra, simple algebra, pre-Lie algebra, mixed identity, bimodule, irreducible bimodule, right-symmetric bimodule, ω-Lie algebra | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
Abstract:
We describe mixed multilinear identities of degree 3 on right endomorphs of arbitrary algebras over a field F of characteristic not equal to 2. As a consequence, we obtain irreducible bimodules over Mn(F) in the variety defined by the monoassociativity identity and in the variety of (1, 1)-algebras. We construct a broad class of right-symmetric bimodules, including irreducible right-symmetric Mn(F)-bimodules. We introduce a class of ω-right-symmetric algebras Aω with an ω-identity, which generalizes the class of right-symmetric algebras, where ω : A×A→ F is a bilinear skew-symmetric form on A. We also describe the structure of finite-dimensional algebras Aω, in particular, simple algebras of this kind. We prove that the commutator algebra A(−) of an arbitrary ω-right-symmetric algebra A is an ω-Lie algebra and that A(−) is solvable of degree ≤ 3 in the finite-dimensional case.
Cite:
Pozhidaev A.P.
On Mixed Identities of Endomorphs, Bimodules, and $ \omega $-Algebras
Siberian Mathematical Journal. 2025. V.66. N4. P.1031-1042. DOI: 10.1134/s0037446625040135 WOS Scopus РИНЦ OpenAlex
On Mixed Identities of Endomorphs, Bimodules, and $ \omega $-Algebras
Siberian Mathematical Journal. 2025. V.66. N4. P.1031-1042. DOI: 10.1134/s0037446625040135 WOS Scopus РИНЦ OpenAlex
Original:
Пожидаев А.П.
О смешанных тождествах эндоморфов, бимодулях ω-алгебрах
Сибирский математический журнал. 2025. Т.66. №4. С.733-746. DOI: 10.33048/smzh.2025.66.413 РИНЦ
О смешанных тождествах эндоморфов, бимодулях ω-алгебрах
Сибирский математический журнал. 2025. Т.66. №4. С.733-746. DOI: 10.33048/smzh.2025.66.413 РИНЦ
Dates:
| Submitted: | Feb 25, 2025 |
| Accepted: | Apr 25, 2025 |
| Published print: | Jul 23, 2025 |
| Published online: | Jul 23, 2025 |
Identifiers:
| Web of science: | WOS:001535187000001 |
| Scopus: | 2-s2.0-105011364322 |
| Elibrary: | 82650984 |
| OpenAlex: | W4412610110 |
Citing:
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