We introduce the class of structurally regular semigroups. Examples of such semigroups are presented, and relationships with other known generalisations of the class of regular semigroups are… Expand

A countable directed family of semigroup congruences is introduced, and a theory analogous to the theory of normal series for groups is developed. This rather simple approach, surprisingly, is an… Expand

The skeleton of the lattice of all structurally trivial semigroup varieties is known to be isomorphic to an infinitely ascending inverted pyramid (Kopamu, 2003). We digitize the skeleton by… Expand

AbstractWe investigate certain semigroup varieties formed by nilpotent extensions of
orthodox normal bands of commutative periodic groups. Such semigroups are shown
to be both structurally periodic… Expand

A semigroup S is said to be structurally regular if there exists an ordered pair (n, m) of non-negative integers such that the quotient S/θ(n, m) is regular in the usual sense. The congruence θ(n, m)… Expand

We introduce in this thesis a new family of semigroup congruences, and we set out to prove that it is worth studying them for the following very important reasons: (a) that it provides an alternative… Expand

Melnik [5] determined completely the lattice of all 2-nilpotent extensions of rectangular band varieties; and Koselev [4] determined a distributive sublattice formed by certain varieties of… Expand