A concept of ideal extensions in ternary semigroups is introduced and throughly investigated. The connection between an ideal extensions and semilattice congruences in ternary semigroups is considered.

In the article we deal with a binary operation that is associative, commutative. We define for such an operation a functor that depends on two more arguments: a finite set of indices and a function indexing elements of the domain of the operation and yields the result of applying the operation to all indexed elements. The definition has a restriction that requires that either the set of indices...

We show that the equational theory of representable lower semilattice-ordered residuated semigroups is finitely based. We survey related results.

We prove that every distributive algebraic lattice with at most א1 compact elements is isomorphic to the normal subgroup lattice of some group and to the submodule lattice of some right module. The א1 bound is optimal, as we find a distributive algebraic lattice D with א2 compact elements that is not isomorphic to the congruence lattice of any algebra with almost permutable congruences (hence n...

The aim of this work is to show how hypergraphs can be used as a systematic tool in the classi!cation of continuous boolean functions according to their degree of parallelism. Intuitively f is “less parallel” than g if it can be de!ned by a sequential program using g as its only free variable. It turns out that the poset induced by this preorder is (as for the degrees of recursion) a sup-semila...

We embed the upper semilattice of r.e. Turing degrees into a slightly larger structure which is better behaved and more foundationally relevant. For P,Q ⊆ 2, we say P is Muchnik reducible to Q if for all Y ∈ Q there exists X ∈ P such that X is Turing reducible to Y . We let Pw denote the lattice of Muchnik degrees of nonempty Π1 subsets of 2. Pw is a countable distributive lattice with 0 and 1....

Let A and B be lattices with zero. The classical tensor product, A ⊗ B, of A and B as join-semilattices with zero is a join-semilattice with zero; it is, in general, not a lattice. We define a very natural condition: A ⊗ B is capped (that is, every element is a finite union of pure tensors) under which the tensor product is always a lattice. Let Conc L denote the join-semilattice with zero of c...