Completions, translational hulls and ideal extensions of inverse semigroups
Hypersubstitutions are mappings which map operation symbols to terms. The set of all hypersubstitutions of a given type forms a monoid with respect to the composition of operations. Together with a second binary operation, to be written as addition, the set of all hypersubstitutions of a given type forms a left-seminearring. Monoids and left-seminearrings of hypersubstitutions can be used to describe complete sublattices of the lattice of all varieties of algebras of a given type. The complexity...
We investigate when a partially ordered semigroup (with various types of local units) is strongly Morita equivalent to a posemigroup from a given class of partially ordered semigroups. Necessary and sufficient conditions for such equivalence are obtained for a series of well-known classes of posemigroups. A number of sufficient conditions for several classes of naturally ordered posemigroups are also provided.