Conditionally complete and conditionally orthogonally complete rings
Conditions for strong Morita equivalence of partially ordered semigroups
We investigate when a partially ordered semigroup (with various types of local units) is strongly Morita equivalent to a posemigroup from a given class of partially ordered semigroups. Necessary and sufficient conditions for such equivalence are obtained for a series of well-known classes of posemigroups. A number of sufficient conditions for several classes of naturally ordered posemigroups are also provided.
Conditions under which the least compactification of a regular continuous frame is perfect
We characterize those regular continuous frames for which the least compactification is a perfect compactification. Perfect compactifications are those compactifications of frames for which the right adjoint of the compactification map preserves disjoint binary joins. Essential to our characterization is the construction of the frame analog of the two-point compactification of a locally compact Hausdorff space, and the concept of remainder in a frame compactification. Indeed, one of the characterizations...
Congruence classes in Brouwerian semilattices
Brouwerian semilattices are meet-semilattices with 1 in which every element a has a relative pseudocomplement with respect to every element b, i. e. a greatest element c with a∧c ≤ b. Properties of classes of reflexive and compatible binary relations, especially of congruences of such algebras are described and an abstract characterization of congruence classes via ideals is obtained.
Congruence extension and amalgamation in C£.
Congruence extension from a semilattice to the freely generated distributive lattice
Congruence factorizations on distributive lattices
Congruence kernels of distributive PJP-semilattices
A meet semilattice with a partial join operation satisfying certain axioms is a JP-semilattice. A PJP-semilattice is a pseudocomplemented JP-semilattice. In this paper we describe the smallest PJP-congruence containing a kernel ideal as a class. Also we describe the largest PJP-congruence containing a filter as a class. Then we give several characterizations of congruence kernels and cokernels for distributive PJP-semilattices.
Congruence kernels of orthoimplication algebras.
Congruence lattices in varieties with compact intersection property
We say that a variety of algebras has the Compact Intersection Property (CIP), if the family of compact congruences of every is closed under intersection. We investigate the congruence lattices of algebras in locally finite, congruence-distributive CIP varieties and obtain a complete characterization for several types of such varieties. It turns out that our description only depends on subdirectly irreducible algebras in and embeddings between them. We believe that the strategy used here can...
Congruence lattices of finite chains with endomorphisms
Characterization of congruence lattices of finite chains with either one or two endomorphisms is given.
Congruence lattices of free lattices in non-distributive varieties
Congruence lattices of intransitive G-Sets and flat M-Sets
An M-Set is a unary algebra whose set of operations is a monoid of transformations of ; is a G-Set if is a group. A lattice is said to be represented by an M-Set if the congruence lattice of is isomorphic to . Given an algebraic lattice , an invariant is introduced here. provides substantial information about properties common to all representations of by intransitive G-Sets. is a sublattice of (possibly isomorphic to the trivial lattice), a -product lattice. A -product...
Congruence lattices of Rees matrix semigroups.
Congruence pairs for algebras abstracting Kleene and Stone algebras
Congruence properties of distributive double -algebras
Congruence relations on and varieties of directed multilattices
Congruence relations on direct products of lattices
Congruence relations on finitary models
Congruence Relations on the Lattice of Partitions in a Set