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Статья
2020

On the Structure of Alternative Bimodules over Semisimple Artinian Algebras


L. R. BorisovaL. R. Borisova, S. V. PchelintsevS. V. Pchelintsev
Русская математика
https://doi.org/10.3103/S1066369X20080010
Abstract / Full Text

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.

Author information
  • Finance University under the Government, 49 Leningradsky Ave., 125993, Moscow, RussiaL. R. Borisova & S. V. Pchelintsev
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