FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 2, PAGES 159-174

Prime radicals of graded W-groups

A. V. Mikhalev
I. N. Balaba
S. A. Pikhtilkov

Abstract

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In this paper, we introduce the class of graded W-groups, which includes: groups; associative, conformal and vertex algebras; Lie algebras and graded algebras. The graded prime radical of a graded W-group is defined, and its elementwise characterization is given. It is shown that the graded prime radical of a graded W-groups with a finiteness condition coincides with the lower weakly solvable (in Parfyonov sense) radical.

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