Geodesic
Prime radicals of graded $\Omega$-groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 2, pp. 159-174.

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In this paper, we introduce the class of graded $\Omega$-groups, which includes: groups; associative, conformal and vertex algebras; Lie algebras and graded algebras. The graded prime radical of a graded $\Omega$-group is defined, and its elementwise characterization is given. It is shown that the graded prime radical of a graded $\Omega$-groups with a finiteness condition coincides with the lower weakly solvable (in Parfyonov sense) radical. 
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A. V. Mikhalev; I. N. Balaba; S. A. Pikhtilkov. Prime radicals of graded $\Omega$-groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 2, pp. 159-174. http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a10/

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