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.
Mots-clés : 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 = {https://geodesic-test.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  - https://geodesic-test.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 https://geodesic-test.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. https://geodesic-test.mathdoc.fr/item/IVM_2020_8_a0/

[1] Eilenberg S., “Extensions of general algebras”, Ann. Soc. Polonaise Math., 21 (1948), 125–134 | MR | Zbl

[2] Schafer R. D., “Representations of alternative algebras”, Trans. Amer. Math. Soc., 72 (1952), 1–17 | DOI | MR | Zbl

[3] Jacobson N., “Structure of alternative and Jordan bimodules”, Osaka J. Math., 6 (1954), 1–71 | MR | Zbl

[4] Svartholm N., “On the algebras of relativistic quantum mechanics”, Proc. Royal Physiographical Soc. Lond., 12 (1942), 94–108 | MR | Zbl

[5] Carlsson R., “Malcev–Moduln”, J. Reine Angeq. Math., 281 (1976), 199–210 | MR | Zbl

[6] Kuzmin E. N., “Algebry Maltseva i ikh predstavleniya”, Algebra i logika, 7 (1968), 48–69 | MR | Zbl

[7] Shestakov I. P., “Pervichnye alternativnye superalgebry proizvolnoi kharakteristiki”, Algebra i logika, 36:6 (1997), 675–716 | MR | Zbl

[8] Murakami L. I., Shestakov I. P., “Irreducible unital right alternative bimodules”, J. Algebra, 246 (2001), 897–914 | DOI | MR | Zbl

[9] Pchelintsev S. V., “Neprivodimye binarno $(-1,1)$-bimoduli nad prostymi konechnomernymi algebrami”, Sib. matem. zhurn., 47:5 (2006), 1139–1146 | MR | Zbl

[10] Shestakov I., Trushina M., “Irreducible bimodules over alternative algebras and superalgebras”, Trans. Amer. Math. Soc., 368:7 (2016), 4657–4684 | DOI | MR | Zbl

[11] Zhevlakov K. A., Slinko A. M., Shestakov I. P., Shirshov A. I., Koltsa, blizkie k assotsiativnym, Nauka, M., 1978 | MR

[12] Kleinfeld E., “Right alternative rings”, Proc. Amer. Math. Soc., 4 (1953), 939–944 | DOI | MR | Zbl

[13] Pchelintsev S. V., “O tsentralnykh idealakh konechno porozhdennykh binarno $(-1,1)$-algebr”, Matem. sb., 193:4 (2002), 113–134 | Zbl

[14] Dzhekobson N., Stroenie kolets, Izd-vo Inlit, M., 1961

[15] Slinko A. M., Shestakov I. P., “Pravye predstavleniya algebr”, Algebra i logika, 13:5 (1974), 544–587 | MR

[16] Jacobson N., Structure and representations of Jordan algebras, Amer. Math. Soc. Colloq. Publ., 39, Amer. Math. Soc., 1968 | MR | Zbl

[17] Solis V. H. L., “Kronecker factorization theorems for alternative superalgebras”, J. Algebra, 528, 311–338 | DOI | MR | Zbl