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...

Electroweak vacuum transition processes (sphalerons) in the early Universe provide a possible explanation of the baryon asymmetry. Combining this physics with the anomalous commutators of Adler and Boulware and renormalization group invariance, we argue that electroweak baryon number violation also induces a “topological condensate” in the vacuum. QCD sphaleron processes act to distribute the b...

A new notion of commutator was defined in any variety of Ω-groups A, relative to any fixed subvariety B of A [1]. This notion gives back the usual commutator of normal subgroups when A is the variety of groups and B the subvariety of abelian groups (see Section 2), but also the Peiffer commutator of normal precrossed submodules, when A is the variety of precrossed modules and B the subvariety o...