Geodesic
Prime algebras and absolute zero divisors
Izvestiya. Mathematics , Tome 28 (1987) no. 1, pp. 79-98.

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

This paper is devoted to the solution of the problem of absolute zero divisors in the varieties of Jordan algebras and $(-1,1)$-algebras over a field of characteristic $0$. It is shown that in those varieties there exist prime algebras generated by absolute zero divisors. Bibliography: 21 titles. 
@article{IM2_1987_28_1_a4,
     author = {S. V. Pchelintsev},
     title = {Prime algebras and absolute zero divisors},
     journal = {Izvestiya. Mathematics },
     pages = {79--98},
     publisher = {mathdoc},
     volume = {28},
     number = {1},
     year = {1987},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1987_28_1_a4/}
}
TY  - JOUR
AU  - S. V. Pchelintsev
TI  - Prime algebras and absolute zero divisors
JO  - Izvestiya. Mathematics 
PY  - 1987
SP  - 79
EP  - 98
VL  - 28
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1987_28_1_a4/
LA  - en
ID  - IM2_1987_28_1_a4
ER  - 
%0 Journal Article
%A S. V. Pchelintsev
%T Prime algebras and absolute zero divisors
%J Izvestiya. Mathematics 
%D 1987
%P 79-98
%V 28
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1987_28_1_a4/
%G en
%F IM2_1987_28_1_a4
S. V. Pchelintsev. Prime algebras and absolute zero divisors. Izvestiya. Mathematics , Tome 28 (1987) no. 1, pp. 79-98. http://geodesic.mathdoc.fr/item/IM2_1987_28_1_a4/

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

[2] Zelmanov E. I., “O pervichnykh iordanovykh algebrakh. II”, Sib. matem. zh., 24:1 (1983), 89–104 | MR

[3] Filippov V. T., “Pervichnye algebry Maltseva”, Matem. zametki, 31:5 (1982), 669–678 | MR | Zbl

[4] Hentzel I. R., “Nil semi-simple (-1,1)-rings”, Algebra, 22:3 (1972), 442–450 | DOI | MR | Zbl

[5] Slater M., “Prime alternative rings. II”, Algebra, 15 (1970), 244–251 | DOI | MR | Zbl

[6] Shestakov I. P., “Absolyutnye deliteli nulya i radikaly konechno porozhdennykh alternativnykh algebr”, Algebra i logika, 15:5 (1976), 585–602 | MR | Zbl

[7] Hentzel I. R., “The characterization of (-1,1)-rings”, Algebra, 30:1–3 (1974), 236–258 | DOI | MR | Zbl

[8] Zelmanov E. I., “Absolyutnye deliteli nulya i algebraicheskie iordanovy algebry”, Sib. matem. zh., 23:6 (1982), 100–116 | MR

[9] Dnestrovskaya tetrad. Nereshennye problemy teorii kolets i modulei, Institut matematiki SO AN SSSR, Novosibirsk, 1982

[10] Zhevlakov K. A., Shestakov I. P., “O lokalnoi konechnosti v smysle Shirshova”, Algebra i logika, 12:1 (1973), 41–73

[11] Pchelintsev S. V., “Absolyutnye deliteli nulya spetsialnykh iordanovykh algebr”, Algebra i logika, 21:6 (1982), 706–720 | MR | Zbl

[12] Jacobson N., Stucture theory of Jordan algebras, University of Arkansas Lecture Notes in Mathematics, 5, 1981 | MR

[13] Pchelintsev S. V., “Primer pervichnoi iordanovoi algebry, porozhdennoi absolyutnymi delitelyami nulya”, Tezisy soobschenii 17-i Vsesoyuznoi algebraicheskoi konferentsii, ch. I, Minsk, 1983, 158

[14] Roomeldi R. E., “Razreshimost (-1,1)-nil-kolets”, Algebra i logika, 12:4 (1973), 478–489 | MR

[15] Roomeldi R. E., “Nizhnii nil-radikal (-1,1)-kolets”, Algebra i logika, 12:3 (1973), 323–332 | MR

[16] Skosyrskii V. G., Radikaly iordanovykh algebr i svyazannykh s nimi assotsiativnykh algebr, Kandidatskaya dissertatsiya, Novosibirsk, 1981

[17] Andrunakievich V. A., Ryabukhin Yu. M., Radikaly algebr i strukturnaya teoriya, Nauka, M., 1979 | MR

[18] Shestakov I. P., “Konechno porozhdennye spetsialnye iordanovy i alternativnye $PI$-algebry”, Matem. sb., 122:1 (1983), 31–40 | MR | Zbl

[19] Latyshev V. N., “K teoreme Regeva o tozhdestvakh tenzornogo proizvedeniya $PI$-algebr”, Uspekhi matem. nauk, 27:4 (1972), 213–214 | MR | Zbl

[20] Pchelintsev S. V., “O metaidealakh alternativnykh algebr”, Sib. matem. zh., 24:3 (1983), 142–148 | MR | Zbl

[21] Markovichev A. S., “Nil-koltsa tipa $(\gamma, \delta)$”, Algebra i logika, 17:2 (1978), 181–200 | MR | Zbl