Title: The inverse hull of 0-left cancellative semigroups,
Abstract: Given a semigroup S with zero, which is left-cancellative in the sense that
st=sr \neq 0 implies that t=r, we construct an inverse semigroup called the
inverse hull of S, denoted H(S). When S admits least common multiples, in a
precise sense defined below, we study the idempotent semilattice of H(S), with
a focus on its spectrum. When S arises as the language semigroup for a subsift
X on a finite alphabet, we discuss the relationship between H(S) and several
C*-algebras associated to X appearing in the literature.