Geodesic
On the structure of alternative bimodules over semisimple artinian algebras
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2020), pp. 3-10

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IVM_2020_8_a0,
     author = {L. R. Borisova and S. V. Pchelintsev},
     title = {On the structure of alternative bimodules over semisimple artinian algebras},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--10},
     publisher = {mathdoc},
     number = {8},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_8_a0/}
}
TY  - JOUR
AU  - L. R. Borisova
AU  - S. V. Pchelintsev
TI  - On the structure of alternative bimodules over semisimple artinian algebras
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2020
SP  - 3
EP  - 10
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2020_8_a0/
LA  - ru
ID  - IVM_2020_8_a0
ER  - 
%0 Journal Article
%A L. R. Borisova
%A S. V. Pchelintsev
%T On the structure of alternative bimodules over semisimple artinian algebras
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2020
%P 3-10
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2020_8_a0/
%G ru
%F IVM_2020_8_a0
L. R. Borisova; S. V. Pchelintsev. On the structure of alternative bimodules over semisimple artinian algebras. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2020), pp. 3-10. http://geodesic.mathdoc.fr/item/IVM_2020_8_a0/