Geodesic
Simple finite-dimensional right-alternative unital superalgebras with strongly associative even part
Sbornik. Mathematics, Tome 208 (2017) no. 4, pp. 531-545 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We prove that the even part of a simple finite-dimensional right-alternative unital superalgebra over a field of characteristic 0 is semisimple if it is strongly associative. Bibliography: 13 titles.
Keywords: simple superalgebra, right-alternative superalgebra, superalgebra with strongly associative even part. 
@article{SM_2017_208_4_a3,
     author = {S. V. Pchelintsev and O. V. Shashkov},
     title = {Simple finite-dimensional right-alternative unital superalgebras with strongly associative even part},
     journal = {Sbornik. Mathematics},
     pages = {531--545},
     year = {2017},
     volume = {208},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_4_a3/}
}
TY  - JOUR
AU  - S. V. Pchelintsev
AU  - O. V. Shashkov
TI  - Simple finite-dimensional right-alternative unital superalgebras with strongly associative even part
JO  - Sbornik. Mathematics
PY  - 2017
SP  - 531
EP  - 545
VL  - 208
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_2017_208_4_a3/
LA  - en
ID  - SM_2017_208_4_a3
ER  - 
%0 Journal Article
%A S. V. Pchelintsev
%A O. V. Shashkov
%T Simple finite-dimensional right-alternative unital superalgebras with strongly associative even part
%J Sbornik. Mathematics
%D 2017
%P 531-545
%V 208
%N 4
%U http://geodesic.mathdoc.fr/item/SM_2017_208_4_a3/
%G en
%F SM_2017_208_4_a3
S. V. Pchelintsev; O. V. Shashkov. Simple finite-dimensional right-alternative unital superalgebras with strongly associative even part. Sbornik. Mathematics, Tome 208 (2017) no. 4, pp. 531-545. http://geodesic.mathdoc.fr/item/SM_2017_208_4_a3/

[1] E. I. Zel'manov, I. P. Shestakov, “Prime alternative superalgebras and the nilpotence of the radical of a free alternative algebra”, Math. USSR-Izv., 37:1 (1991), 19–36 | DOI | MR | Zbl

[2] J. Picanço da Silva, L. S. I. Murakami, I. Shestakov, “On right alternative syperalgebras”, Comm. Algebra, 44:1 (2016), 240–252 | DOI | MR | Zbl

[3] K. A. Zhevlakov, A. M. Slin'ko, I. P. Shestakov, A. I. Shirshov, Rings that are nearly associative, Pure Appl. Math., 104, Academic Press, Inc., New York–London, 1982, xi+371 pp. | MR | MR | Zbl | Zbl

[4] S. V. Pchelintsev, O. V. Shashkov, “Simple finite-dimensional right alternative superalgebras with unitary even part over a field of characteristic $0$”, Math. Notes, 100:4 (2016), 589–596 | DOI | DOI | MR | Zbl

[5] N. Jacobson, Structure and representations of Jordan algebras, Amer. Math. Soc. Colloq. Publ., 39, Amer. Math. Soc., Providence, RI, 1968, x+453 pp. | MR | Zbl

[6] S. V. Pchelintsev, O. V. Shashkov, “Simple finite-dimensional right-alternative superalgebras of Abelian type of characteristic zero”, Izv. Math., 79:3 (2015), 554–580 | DOI | DOI | MR | Zbl

[7] S. V. Pchelintsev, O. V. Shashkov, “Simple right alternative superalgebras of Abelian type whose even part is a field”, Izv. Math., 80:6 (2016), 1231–1241 | DOI | DOI | MR

[8] S. V. Pchelintsev, O. V. Shashkov, “Prostye konechnomernye pravoalternativnye superalgebry s poluprostoi silno assotsiativnoi chetnoi chastyu”, Matem. sb., 208:2 (2017), 55–69 | DOI | MR

[9] C. T. C. Wall, “Graded Brauer groups”, J. Reine Angew. Math., 1964:213 (1964), 187–199 | DOI | MR | Zbl

[10] V. N. Zhelyabin, “Simple special Jordan superalgebras with associative nil-semisimple even part”, Algebra and Logic, 41:3 (2002), 152–172 | DOI | MR | Zbl

[11] V. N. Zhelyabin, “Simple Jordan superalgebras with associative nil-semisimple even part”, Siberian Math. J., 57:6 (2016), 987–1001 | DOI | DOI

[12] E. Kleinfeld, “Right alternative rings”, Proc. Amer. Math. Soc., 4:6 (1953), 939–944 | DOI | MR | Zbl

[13] T. Anderson, “Hereditary radicals and derivations of algebras”, Canad. J. Math., 21 (1969), 372–377 | DOI | MR | Zbl