A type of product for uniform semilattices

Uniform semilattices can be characterized as the semilattices of bisimple inverse semigroups 4,5]. This motivates the study of such semilattices. In particular, we may consider ways of forming uniform semilattices by combining together known ones. In this paper, we give a construction which, given two suitable semilattices, produces another semilattice, their so-called link product. The construction may be used to obtain uniform semilattices and, in particular, yields a family of pairwise non-isomorphic uniform semilattices M(r), indexed by the non-negative integer r. It is our intention to discuss in a further paper the structure of bisimple inverse semigroups with semilattice isomorphic to M(r).