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Izv. Vyssh. Uchebn. Zaved. Mat., 2020, Number 8, Pages 3–10 (Mi ivm9598)  

On the structure of alternative bimodules over semisimple artinian algebras

L. R. Borisova, S. V. Pchelintsev

Finance University under the Government, 49 Leningradsky Ave., Moscow, 125993 Russia

Abstract: The alternative bimodules over semisimple artinian algebras are studied. A bimodule is called almost reducible if it is a direct sum of an associative subbimodule and a completely reducible subbimodule. It is proved that if a semisimple algebra cannot be homomorphically mapped onto a associative division algebra, then an alternative bimodule above it is almost reducible. An example of an alternative bimodule over a field of rational functions of two variables, which is not almost reducible, is given.

Keywords: alternative algebra, irreducible bimodule, almost reducible bimodule.

DOI: https://doi.org/10.26907/0021-3446-2020-8-3-10

Full text: PDF file (350 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2020, 64:8, 1–7

Bibliographic databases:

UDC: 512.554
Received: 08.10.2019
Revised: 13.12.2019
Accepted: 18.12.2019

Citation: L. R. Borisova, S. V. Pchelintsev, “On the structure of alternative bimodules over semisimple artinian algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 8, 3–10; Russian Math. (Iz. VUZ), 64:8 (2020), 1–7

Citation in format AMSBIB
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\paper On the structure of alternative bimodules over semisimple artinian algebras
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
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\issue 8
\pages 3--10
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\crossref{https://doi.org/10.26907/0021-3446-2020-8-3-10}
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\jour Russian Math. (Iz. VUZ)
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\vol 64
\issue 8
\pages 1--7
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