On some presentations of completely regular semigroups

In this paper we consider three types of presentations of completely regular semigroups. In each of the considered cases the solution of the word problem can be reduced to the solution of the word problem for a corresponding group presentation. As a consequence, in each of these cases the one relator presentation has a solvable word problem.     

On some classes of infinitely differentiable operator semigroups

Given a linear relation (a multivalued linear operator), we construct an infinitely differentiable operator semigroup and study its properties.     

On some intervals of varieties of completely regular semigroups

Semigroup Forum - Completely regular semigroups with the unary operation of inversion within their maximal subgroups form a variety under inclusion denoted by $$mathcal {C}mathcal {R}$$. The...     

On associate subgroups of regular semigroups

We describe the structure of a regular semigroup with an associate subgroup the identiy element of which is a mcdial idempotent. As a particular application of this, we obtain the structure of perfect Dubreil-Jacotin semigroups in which the set of residuals of the bimaximum element form a subgroup.     

On varieties of completely regular semigroups III

Communicated by J.M. Howie     

Characterizations of some classes of relatively regular operators

A bounded linear operator A on a Banach space is called relatively regular, if there is a bounded linear operator B such that ABA=A. In this case B is called a g₁-inverse of A. In this paper we characterize some classes of relatively regular operators A via the set {B₁-B₂:B₁ and B₂ are g₁-inverses of A}.     

On some classes of regular linear extensions of dynamical systems on a torus

We select some classes of linear extensions of dynamical systems on a torus for which weak regularity implies regularity.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 11, pp. 1479–1485, November, 1994.This work was supported by the Ukrainian State Committee on Science and Technology.