We investigate commutator operations on compatible uniformities. We present a commutator operation for uniformities in the congruence-modular case which extends the commutator on congruences, and explore its properties. Introduction The purpose of this paper is to generalize the commutator of congruences to a commutator of compatible uniformities. Commutator theory (on congruences) works best f...

We develop the theories of the strong commutator, the rectangular commutator, the strong rectangular commutator, as well as a solvability theory for the nonmodular TC commutator. These theories are used to show that each of the following sets of statements are equivalent for a variety V of algebras. (I) (a) V satisfies a nontrivial congruence identity. (b) V satisfies an idempotent Maltsev cond...

In this paper, we verify the solvability of free product of finite cyclic groups with topological methods. We use Cayley graphs and Everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator subgroups. In particular, using these methods, we prove that the commutator subgroup of $mathbb{Z}_{m}*mathbb{Z}_{n}$ is free of rank $(m-1)(n-1)$ fo...

Let T be a contraction and A the strong limit of {T∗nTn}n≥1. We prove the following theorem: if a hyponormal contraction T does not have a nontrivial invariant subspace, then T is either a proper contraction of class 00 or a nonstrict proper contraction of class 10 for which A is a completely nonprojective nonstrict proper contraction. Moreover, its self-commutator [T∗,T ] is a strict contracti...

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.

Abstract A super Jaulent-Miodek hierarchy and its super Hamiltonian structures are constructed by means of a kind of Lie super algebras and super trace identity. Moreover, the self-consistent sources of the super Jaulent-Miodek hierarchy is presented based on the theory of self-consistent sources. Furthermore, the infinite conservation laws of the super Jaulent-Miodek hierarchy are also obtaine...