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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 areExpand
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On semigroup species
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 anExpand
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Varieties of Structurally Trivial Semigroups III
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 byExpand
Varieties and Nilpotent Extensions of Permutative Periodic Semigroups
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 periodicExpand
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The Class of Structurally Regular Semigroups
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
On a family of semigroup congruences
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 alternativeExpand
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Varieties of structurally trivial semigroups II
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 ofExpand
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