Abstract. For any finite unital commutative idempotent semigroup S, a unital semilattice, we show how to compute the amenability constant of its semigroup algebra l(S), which is always of the form 4n+1. We then show that these give lower bounds to amenability constants of certain Banach algebras graded over semilattices. Our theory applies to certain natural subalgebras of Fourier-Stieltjes alg...

Today, the theoretical framework of mathematical morphology is phrased in terms of complete lattices and operators de ned on them. That means in particular that the choice of the underlying partial ordering is of eminent importance, as it determines the class of morphological operators that one ends up with. The duality principle for partially ordered sets, which says that the opposite of a par...

We define the tensor product A ® S for arbitrary semilattices A and B. The construction is analogous to one used in ring theory (see 14], [7], [8]) and different from one studied by A. Waterman [12], D. Mowat [9], and Z. Shmuely [10]. We show that the semilattice A <3 B is a distributive lattice whenever A and B are distributive lattices, and we investigate the relationship between the Stone sp...

This article is the second of two presenting a new approach to left adequate monoids. In the first, we introduced the notion of being T -proper, where T is a submonoid of a left adequate monoid M . We showed that the free left adequate monoid on a set X is X∗-proper. Further, any left adequate monoid M has an X∗-proper cover for some set X , that is, there is an X∗proper left adequate monoid M̂ ...

We show that for every quasivariety K of relational structures there is a semilattice S with operators such that the lattice of quasiequational theories of K (the dual of the lattice of sub-quasivarieties of K) is isomorphic to Con(S,+, 0, F). As a consequence, new restrictions on the natural quasi-interior operator on lattices of quasi-equational theories are found. 1. Motivation and terminolo...