On Z6-graded Lie rings

A Nilpotent Quotient Algorithm for Graded Lie Rings

A nilpotent quotient algorithm for graded Lie rings of prime characteristic is described. The algorithm has been implemented and applications have been made to the investigation of the associated Lie rings of Burnside groups. New results about Lie rings and Burnside groups are presented. These include detailed information on groups of exponent 5 and 7 and their associated Lie rings. Appeared: J...

On Rings Whose Associated Lie Rings Are Nilpotent

We call (i?) 1 the Lie ring associated with R, and denote it by 9Î. The question of how far the properties of SR determine those of R is of considerable interest, and has been studied extensively for the case when R is an algebra, but little is known of the situation in general. In an earlier paper the author investigated the effect of the nilpotency of 9î upon the structure of R if R contains ...

On Associated Graded Rings of Normal Ideals

Semisimple Strongly Graded Rings

Let G be a finite group and R a strongly G-graded ring. The question of when R is semisimple (meaning in this paper semisimple artinian) has been studied by several authors. The most classical result is Maschke’s Theorem for group rings. For crossed products over fields there is a satisfactory answer given by Aljadeff and Robinson [3]. Another partial answer for skew group rings was given by Al...

Graded Rings and Modules

1 Definitions Definition 1. A graded ring is a ring S together with a set of subgroups Sd, d ≥ 0 such that S = ⊕ d≥0 Sd as an abelian group, and st ∈ Sd+e for all s ∈ Sd, t ∈ Se. One can prove that 1 ∈ S0 and if S is a domain then any unit of S also belongs to S0. A homogenous ideal of S is an ideal a with the property that for any f ∈ a we also have fd ∈ a for all d ≥ 0. A morphism of graded r...