On compact classes of models
On compatible and order-preserving functions on lattices
On completions of partial monounary algebras
On congruence distributivity of ordered algebras with constants
We define the order-congruence distributivity at 0 and order- congruence n-distributivity at 0 of ordered algebras with a nullary operation 0. These notions are generalizations of congruence distributivity and congruence n-distributivity. We prove that a class of ordered algebras with a nullary operation 0 closed under taking subalgebras and direct products is order-congruence distributive at 0 iff it is order-congruence n-distributive at 0. We also characterize such classes by a Mal'tsev condition....
On congruence lattices in a category
On congruence lattices of finite partial unary algebras
On congruence lattices of regular semigroups with Q-inverse transversals.
On congruence relations of monounary algebras. I
On congruence relations of monounary algebras. II
On congruences in direct sums of algebras
On congruences of -sets
We describe -sets whose congruences satisfy some natural lattice or multiplicative restrictions. In particular, we determine -sets with distributive, arguesian, modular, upper or lower semimodular congruence lattice as well as congruence -permutable -sets for .
On congruences of ...x-normal semigroups.
On connected unars with regular endomorphism monoids
On connections between hypergraphs and algebras
The aim of the present paper is to translate some algebraic concepts to hypergraphs. Thus we obtain a new language, very useful in the investigation of subalgebra lattices of partial, and also total, algebras. In this paper we solve three such problems on subalgebra lattices, other will be solved in [[Pio4]]. First, we show that for two arbitrary partial algebras, if their directed hypergraphs are isomorphic, then their weak, relative and strong subalgebra lattices are isomorphic. Secondly, we prove...
On connections between the decomposition of an algebra into sums of direct systems of subalgebras
On convexities of lattices
On countably compact reduced products, III
On countably universal Boolean algebras compact classes of models
On covarieties of coalgebras
On covariety lattices
This paper shows basic properties of covariety lattices. Such lattices are shown to be infinitely distributive. The covariety lattice of subcovarieties of a covariety K of F-coalgebras, where F:Set → Set preserves arbitrary intersections is isomorphic to the lattice of subcoalgebras of a -coalgebra for some cardinal κ. A full description of the covariety lattice of Id-coalgebras is given. For any topology τ there exist a bounded functor F:Set → Set and a covariety K of F-coalgebras, such that...