Note on unipotent inversible semigroups

A Note on Extending Semicharacters on Semigroups

The purpose of this note is to give a necessary and sufficient condition for a semicharacter on a subsemigroup of a commutative semigroup G to be extendable to a semicharacter on G. A bounded complex function x on a semigroup G is called a semicharacter of G if x(x)9^0 for some xEG and x(xy) = x(%)x(y) ior all x, yEG. Semicharacters were introduced by Hewitt and Zuckerman [l] and in a slightly ...

A note on infinitely distributive inverse semigroups

By an infinitely distributive inverse semigroup will be meant an inverse semigroup S such that for every subset X ⊆ S and every s ∈ S, if ∨ X exists then so does ∨ (sX), and furthermore ∨ (sX) = s ∨ X. One important aspect is that the infinite distributivity of E(S) implies that of S; that is, if the multiplication of E(S) distributes over all the joins that exist in E(S) then S is infinitely d...

A Note on Representations of Inverse Semigroups

It is known [l; 2] that every inverse semigroup 5 has a faithful representation as a semigroup of (1, l)-mappings of subsets of a set A into A. The set A may be taken as the set of elements of 5 and the (1, l)-mappings as mappings of principal left ideals of 5 onto principal left ideals of 5. If £ is the set of idempotents of 5 then there is also a representation of 5, not necessarily faithful,...

A Note on Amalgams of Inverse Semigroups

A Note on Complex Algebras of Semigroups

The main result is that the variety generated by complex algebras of (commutative) semigroups is not finitely based. It is shown that this variety coincides with the variety generated by complex algebras of partial (commutative) semigroups. An example is given of an 8-element commutative Boolean semigroup that is not in this variety, and an analysis of all smaller Boolean semigroups shows that ...