We give a general description of the free proonite semigroups over a semidirect product of pseudovarieties. More precisely, A (V W) is described as a closed subsemigroup of a proonite semidirect product of the form A WA V A W. As a particular case, the free proonite semigroup over J 1 V is described in terms of the geometry of the Cayley graph of the free proonite semigroup over V (here J 1 is ...

Plotkin [1976] introduced a powerdomain construction on domains in order to give semantics to a non-deterministic binary choice constructor, and later [1979] characterised it as the free semilattice. Smyth [1983] and Winskel [1985] showed that it could be interpreted in terms of modal predicate transformers and Robinson [1986] recognised it as a special case of Johnstone’s [1982] Vietoris const...

The main purpose of this paper is to show that a regular semigroup S is a semilattice of bisimple semigroups if and only if it is a band of bisimple semigroups and that this holds if and only if 3) is a congruence on S. It is also shown that a quasiregular semigroup 5 which is a rectangular band of bisimple semigroups is itself bisimple. In [3, Theorem 4.4] it was shown that a semigroup S is a ...

We study the stability and the stability index of themeet game form defined on a meet-semilattice. Given any active coalition structure, we show that the stability index relative to the equilibrium, to the beta core and to the exact core is a function of the Nakamura number, the depth of the semilattice and its gap function.

We show that no finite set of first-order axioms can define the class of representable semilattice-ordered monoids.

We exhibit some new connections between structure of an information system and its corresponding semilattice of equivalence relations. In particular, we investigate dependency properties and introduce a partial ordering of information systems over a fixed object set U which reflects the sub–semilattice relation on the set of all equivalence relations on U.

We show that a locally finite variety which omits abelian types is self–rectangulating if and only if it has a compatible semilattice term operation. Such varieties must have type–set {5 }. These varieties are residually small and, when they are finitely generated, they have definable principal congruences. We show that idempotent varieties with a compatible semilattice term operation have the ...

A specialization semilattice is a structure which can be embedded into $(\mathcal P(X), \cup, \sqsubseteq )$, where $X$ topological space, $ x y$ means $x \subseteq Ky$, for $x,y X$, and $K$ closure in $X$. Specialization semilattices posets appear as auxiliary structures many disparate scientific fields, even unrelated to topology. In general, not expressible semilattice. On the other hand, we...

Canonical extensions of (bounded) lattices have been extensively studied, and the basic existence and uniqueness theorems for these have been extended to general posets. This paper focuses on the intermediate class S∧ of (unital) meet semilattices. Any S ∈ S∧ embeds into the algebraic closure system Filt(Filt(S)). This iterated filter completion, denoted Filt(S), is a compact and ∨∧ -dense exte...