The prime radical of alternative rings and loops
Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 1, pp. 145-166.

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

A characterization of the prime radical of loops as the set of strongly Engel elements was given in our earlier paper. In this paper, some properties of the prime radical of loops are considered. Also a connection between the prime radical of the loop of units of an alternative ring and the prime radical of this ring is given.
@article{FPM_2015_20_1_a7,
     author = {A. V. Gribov},
     title = {The prime radical of alternative rings and loops},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {145--166},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2015_20_1_a7/}
}
TY  - JOUR
AU  - A. V. Gribov
TI  - The prime radical of alternative rings and loops
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2015
SP  - 145
EP  - 166
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2015_20_1_a7/
LA  - ru
ID  - FPM_2015_20_1_a7
ER  - 
%0 Journal Article
%A A. V. Gribov
%T The prime radical of alternative rings and loops
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2015
%P 145-166
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2015_20_1_a7/
%G ru
%F FPM_2015_20_1_a7
A. V. Gribov. The prime radical of alternative rings and loops. Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 1, pp. 145-166. http://geodesic.mathdoc.fr/item/FPM_2015_20_1_a7/

[1] Beidar K. I., Mikhalëv A. V., Slinko A. M., “Kriterii pervichnosti dlya nevyrozhdennykh alternativnykh i iordanovykh algebr”, Tr. MMO, 50, 1987, 130–137 | MR | Zbl

[2] Belousov V. D., Osnovy teorii kvazigrupp i lup, Nauka, M., 1967 | MR

[3] Gribov A. V., Mikhalëv A. V., “Pervichnyi radikal dlya lup i $\Omega$-lup. I”, Fundament. i prikl. matem., 19:2 (2014), 25–42

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

[5] Zelmanov E. I., “Pervichnye alternativnye superalgebry i nilpotentnost radikala svobodnoi alternativnoi algebry”, Izv. AN SSSR. Ser. matem., 54:4 (1990), 676–693 | MR | Zbl

[6] Kurosh A. G., “Radikaly kolets i algebr”, Matem. sb., 33(75):1 (1953), 13–26 | MR | Zbl

[7] Skornyakov L. A., “Pravo-alternativnye tela”, Izv. AN SSSR. Ser. matem., 15:2 (1951), 177–184 | MR | Zbl

[8] Schukin K. K., “RI$^*$-razreshimyi radikal grupp”, Matem. sb., 52:4 (1960), 1021–1031 | MR | Zbl

[9] Bruck R., A Survey of Binary Systems, Springer, Berlin, 1958 | MR | Zbl

[10] Goodaire E. G., Jespers E., Polcino Miles C., Alternative Loop Rings, Elsevier, Amsterdam, 1996

[11] Levitzki J., “Prime ideals and the lower radical”, Amer. J. Math., 73 (1951), 25–29 | DOI | MR | Zbl

[12] Pflugfelder H., Quasigroups and Loops: Introduction, Sigma Ser. Pure Math., 7, Heldermann, 1991 | MR

[13] Rich M., “Some radical properties of $s$-rings”, Proc. Amer. Math. Soc., 30:1 (1971), 40–42 | MR | Zbl

[14] Rich M., “The prime radical in alternative rings”, Proc. Amer. Math. Soc., 56 (1976), 11–15 | DOI | MR | Zbl

[15] Stanovsky D., Vojtechovsky P., “Commutator theory for loops”, J. Algebra, 399 (2014), 290–322 | DOI | MR | Zbl

[16] Tsai C., “The prime radical in a Jordan ring”, Proc. Amer. Math. Soc., 19 (1968), 1171–1175 | DOI | MR | Zbl