Geodesic
Differentiably simple alternative algebras
Algebra i logika, Tome 49 (2010) no. 5, pp. 670-689.

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

Differentiably simple alternative nonassociative algebras of characteristic $p>0$ are described in terms of differentiably simple associative commutative algebras. Also we look at some properties of differentiably simple alternative nonassociative algebras of characteristic $0$.
Keywords: alternative algebra, Cayley–Dixon ring, Cayley–Dixon algebra, derivation, differentiably simple algebra. 
@article{AL_2010_49_5_a5,
     author = {A. A. Popov},
     title = {Differentiably simple alternative algebras},
     journal = {Algebra i logika},
     pages = {670--689},
     publisher = {mathdoc},
     volume = {49},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2010_49_5_a5/}
}
TY  - JOUR
AU  - A. A. Popov
TI  - Differentiably simple alternative algebras
JO  - Algebra i logika
PY  - 2010
SP  - 670
EP  - 689
VL  - 49
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2010_49_5_a5/
LA  - ru
ID  - AL_2010_49_5_a5
ER  - 
%0 Journal Article
%A A. A. Popov
%T Differentiably simple alternative algebras
%J Algebra i logika
%D 2010
%P 670-689
%V 49
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2010_49_5_a5/
%G ru
%F AL_2010_49_5_a5
A. A. Popov. Differentiably simple alternative algebras. Algebra i logika, Tome 49 (2010) no. 5, pp. 670-689. http://geodesic.mathdoc.fr/item/AL_2010_49_5_a5/

[1] E. C. Posner, “Differentiable simple rings”, Proc. Am. Math. Soc., 11:3 (1960), 337–343 | DOI | MR | Zbl

[2] L. R. Harper (jun.), “On differentiably simple algebras”, Trans. Am. Math. Soc., 100:1 (1961), 63–72 | DOI | MR | Zbl

[3] S. Yuan, “Differentiably simple rings of prime characteristic”, Duke Math. J., 31 (1964), 623–630 | DOI | MR | Zbl

[4] R. E. Block, “Determination of the differentiably simple rings with a minimal ideal”, Ann. Math. (2), 90:3 (1969), 433–459 | DOI | MR | Zbl

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

[6] A. M. Slinko, “Zamechanie o radikalakh i differentsiirovaniyakh kolets”, Sib. matem. zh., 13:6 (1972), 1395–1397 | MR

[7] R. D. Schafer, An introduction to nonassociative algebras, Pure Appl. Math., 22, Academic Press, New York–London, 1966 | MR | Zbl

[8] N. Jacobson, “A Kronecker factorization theorem for Cayley algebras and the exceptional simple Jordan algebra”, Am. J. Math., 76 (1954), 447–452 | DOI | MR | Zbl

[9] G. Azumaya, “On maximally central algebras”, Nagoya Math. J., 2 (1951), 119–150 | MR | Zbl

[10] N. Burbaki, Kommutativnaya algebra, Mir, M., 1971 | MR