Geodesic
Сentral orders in simple finite dimensional superalgebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1027-1042.

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

The well-known Formanek's module finiteness theorem states that every unital prime PI-algebra (i.e. a central order in a matrix algebra by Posner's theorem) embeds into a finitely generated module over its center. An analogue of this theorem for alternative and Jordan algebras was earlier proved by V.N. Zhelyabin and the author. In this paper we discuss this problem for associative, classical Jordan and some alternative superalgebras.
Keywords: central order, associative superalgebra, alternatve superalgebra, Jordan superalgebra, simple superalgebra. 
@article{SEMR_2020_17_a23,
     author = {A. S. Panasenko},
     title = {{\CYRS}entral orders in simple finite dimensional superalgebras},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1027--1042},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a23/}
}
TY  - JOUR
AU  - A. S. Panasenko
TI  - Сentral orders in simple finite dimensional superalgebras
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2020
SP  - 1027
EP  - 1042
VL  - 17
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2020_17_a23/
LA  - en
ID  - SEMR_2020_17_a23
ER  - 
%0 Journal Article
%A A. S. Panasenko
%T Сentral orders in simple finite dimensional superalgebras
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2020
%P 1027-1042
%V 17
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2020_17_a23/
%G en
%F SEMR_2020_17_a23
A. S. Panasenko. Сentral orders in simple finite dimensional superalgebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1027-1042. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a23/

[1] E. Posner, “Prime rings satisfying a polynomial identity”, Proc. Am. Math. Soc., 11 (1960), 180–183 | DOI | MR | Zbl

[2] M. Slater, “Prime alternative rings III”, J. Algebra, 21:3 (1972), 394–409 | DOI | MR | Zbl

[3] E.I. Zel'manov, “Prime Jordan algebras II”, Sib. Math. J., 24 (1983), 73–85 | DOI | Zbl

[4] I.P. Shestakov, “Prime alternative superalgebras of arbitrary characteristic”, Algebra Logic, 36:6 (1997), 389–412 | DOI | MR | Zbl

[5] E. Formanek, “Noetherian PI-rings”, Commun. Algebra, 1:1 (1974), 79–86 | DOI | MR | Zbl

[6] A.S. Panasenko, “Just infinite alternative algebras”, Math. Notes, 98:5 (2015), 805–812 | DOI | MR | Zbl

[7] V.N. Zhelyabin, A.S. Panasenko, “Nearly finite-dimensional Jordan algebras”, Algebra Logic, 57:5 (2018), 336–352 | DOI | MR | Zbl

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

[9] V.N. Zhelyabin, A.S. Zakharov, “Some constructions for Jordan superalgebras with associative even part”, St. Petersbg. Math. J., 28:2 (2017), 197–208 | DOI | MR | Zbl

[10] V.N. Zhelyabin, “Structure of some unital simple Jordan superalgebras with associative even part”, Sib. Math. J., 59:6 (2018), 1051–1062 | DOI | MR | Zbl

[11] F.A. Gomez Gonzalez, R. Velasquez, “Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem”, Algebra Discrete Math., 26:1 (2018), 19–33 | MR | Zbl

[12] F.A. Gomez Gonzalez, “Jordan superalgebras of type $M_{n|m}(F)^{(+)}$ and the Wedderburn Principal Theorem (WPT)”, Commun. Algebra, 44:7 (2016), 2867–2886 | DOI | MR | Zbl

[13] F.A. Gomez Gonzalez, “Wedderburn principal theorem for Jordan superalgebras I”, J. Algebra, 505 (2018), 1–32 | DOI | MR | Zbl

[14] F.A. Gomez Gonzalez, “Jordan superalgebra of type $JP_n$, $n\ge 3$ and the Wedderburn principal theorem”, Commun. Algebra, 48:5 (2020), 2258–2266 | DOI | MR | Zbl

[15] M.L. Racine, E.I. Zel'manov, “Simple Jordan superalgebras with semisimple even part”, J. Algebra, 270:2 (2003), 374–444 | DOI | MR | Zbl

[16] M.L. Racine, “Primitive superalgebras with superinvolution”, J. Algebra, 206:2 (1998), 588–614 | DOI | MR | Zbl

[17] I.N. Herstein, Noncommutative Rings, The Carus Mathematical Monograph, 15, Wiley and Sons, 1968 | MR | Zbl

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

[19] K.A. Zhevlakov, A.M. Slinko, I.P. Shestakov, A.I. Shirshov, Rings that are nearly associative, Academic Press, New York etc, 1982 | MR | Zbl