Representable divisibility semigroups
Bruno Bosbach · Proceedings of the Edinburgh Mathematical Society · 1991
By a divisibility semigroup we mean an algebra (S,., ∧) satisfying (Al) (S,.) is a semigroup; (A2) (S, ∧) is a semilattice; (A3) . A divisibility semigroup is called representable if it admits a subdirect decomposition into totally ordered factors. In this paper various types of representable divisibility semigroups are investigated and characterized, admitting a representation in general or even a special decomposition, like subdirect sums of archimedean factors, for instance.