A note on free inverse semigroups

A Note on Amalgams of Inverse Semigroups

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 STRONGLY E-REFLEXrVE INVERSE SEMIGROUPS

In contrast to the semilattice of groups case, an inverse semigroup S which is the union of strongly ^-reflexive inverse subsemigroups need not be strongly £-reflexive. If, however, the union is saturated with respect to the Green's relation <3), and in particular if the union is a disjoint one, then 5 is indeed strongly £-reflexive. This is established by showing that fy -saturated inverse sub...

Amalgams of Free Inverse Semigroups

We study inverse semigroup amalgams of the form S U T where S and T are free inverse semigroups and U is an arbitrary nitely generated inverse subsemigroup of S and T. We make use of recent work of Bennett to show that the word problem is decidable for any such amalgam. This is in contrast to the general situation for semigroup amalgams, where recent work of Birget, Margolis and Meakin shows th...