A note on amalgams of inverse semigroups

A Note on Amalgams of Inverse Semigroups

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...

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 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...

Amalgams of inverse semigroups and reversible two-counter machines

We show that the word problem for an amalgam [S1, S2;U,ω1, ω2] of inverse semigroups may be undecidable even if we assume S1 and S2 (and therefore U) to have finite R-classes and ω1, ω2 to be computable functions, interrupting a series of positive decidability results on the subject. This is achieved by encoding into an appropriate amalgam of inverse semigroups 2-counter machines with sufficien...