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 an 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.
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Russian Text © The Author(s), 2020, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, No. 8, pp. 3–10.
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Borisova, L.R., Pchelintsev, S.V. On the Structure of Alternative Bimodules over Semisimple Artinian Algebras. Russ Math. 64, 1–7 (2020). https://doi.org/10.3103/S1066369X20080010
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DOI: https://doi.org/10.3103/S1066369X20080010