A skew lattice is a noncommutative associative analogue of a lattice and as such may be viewed both as an algebraic object and as a geometric ob- ject. Whereas recent papers on skew lattices… Expand

There is a substantial theory (modelled on permutation representations of groups) of representations of an
inverse semigroup S in a symmetric inverse monoid I_X , that is, a monoid of partial… Expand

We examine cancellation in skew lattices, where the involved objects are in many ways lattice-like, but the operations $\land$ and $\lor$ no longer need be commutative.Expand

An inverse semigroup is a semigroup S such that for each x e S there exists a unique inverse x~ & S such that both xx~x=x and x~xx~=x~\ This condition is equivalent to S both being (von Neumann)… Expand

Distributive skew lattices satisfying $$x\wedge (y\vee z)\wedge x = (x\wedge y\wedge x) \vee (x\wedge z\wedge x)$$x∧(y∨z)∧x=(x∧y∧x)∨(x∧z∧x) and its dual are studied, along with the larger class of… Expand