Lie isomorphisms of derived rings of simple rings

Isomorphisms of p-adic group rings

A long-standing problem, first posed by Graham Higman [15] and later by Brauer [4] is the “isomorphism problem for integral group rings.” Given finite groups G and H, is it true that ZG = ZH implies G 2: H? Many authors have worked on this question, but progress has been difficult [30]. Perhaps the best positive result was that of Whitcomb in 1968 [37], who showed that the implication G = H hol...

Prime Lie Rings of Generalized Derivations of Commutative Rings

Let R be a commutative ring with identity. By a Bres̃ar generalized derivation of R we mean an additive map g : R→ R such that g (xy) = g (x) y + xd (y) for all x, y ∈ R, where d is a derivation of R. And an additive mapping f : R → R is called a generalized derivation in the sense of Nakajima if it satisfies f(xy) = f(x)y + xf(y) − xf(1)y for all x, y ∈ R. In this paper we extend some results o...

Representation Rings of Lie Superalgebras

Given a Lie superalgebra g, we introduce several variants of the representation ring, built as subrings and quotients of the ring RZ2(g) of virtual g-supermodules, up to (even) isomorphisms. In particular, we consider the ideal R+(g) of virtual g-supermodules isomorphic to their own parity reversals, as well as an equivariant K-theoretic super representation ring SR(g) on which the parity rever...

Lie and Jordan Structures in Simple, Associative Rings

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 ...