It is proved that certain rings satisfying generalized-commutator constraints of the form [x n n n y y y 0 with m and n depending on x and y, mst have nll commutator ideal. KEY WDRDS AND PHRASES. Commutator ideal, periodic ring. 1980 AMS SUBJECT CLASSIFICATION CODE. 16A70.

A classification of the ways in which an element of a free group can be expressed as a product of commutators or as a product of squares is given. This is then applied to some particular classes of elements. Finally, a question about expressing a commutator as a product of squares is addressed.

We study the general form of the * –commutator treated as a deformation of the Poisson bracket on the Grassman algebra. We show that, up to a similarity transformation , there are other deformations of the Poisson bracket in addition to the Moyal commutator (one at even and one at odd n, n is the number of the generators of the Grassman algebra) which are not reduced to the Moyal commutator by ...

Based on the concept of double central extension from categorical Galois theory, we study a notion of commutator which is defined relative to a Birkhoff subcategory B of a semi-abelian category A. This commutator characterises Janelidze and Kelly’s B-central extensions; when the subcategoryB is determined by the abelian objects inA, it coincides with Huq’s commutator; and when the category A is...

Let G be the first Grigorchuk group. We show that the commutator width of G is 2: every element g ∈ [G, G] is a product of two commutators, and also of six conjugates of a. Furthermore, we show that every finitely generated subgroup H ≤ G has finite commutator width, which however can be arbitrarily large, and that G contains a subgroup of infinite commutator width. The proofs were assisted by ...

Commutator errors arise in large-eddy simulation of incompressible turbulent flow from the application of non-uniform filters to the continuity – and Navier– Stokes equations. For non-uniform, high order filters with bounded moments the magnitude of the commutator errors is shown to be of the same order as that of the turbulent stress fluxes. Consequently, one cannot reduce the size of the comm...