Semimodularity and weak modularity in subalgebra lattices of completely simple semigroups.
Semiregularity of congruences implies congruence modularity at 0
We introduce a weakened form of regularity, the so called semiregularity, and we show that if every diagonal subalgebra of is semiregular then is congruence modular at 0.
Simplicity of algebras requires to investigate almost all operations
Some decidable congruences of free monoids
Let be the free monoid over a finite alphabet . We prove that a congruence of generated by a finite number of pairs , where and , is always decidable.
Some finite congruence lattices, I
Some modifications of congruence permutability and dually congruence regular varietie
It is well known that every congruence regular variety is n-permutable (in the sense of [9]) for some n ≥ 2. For the explicit proof see e.g. [2]. The connections between this n and Mal'cev type characterizations of congruence regularity were studied by G.D. Barbour and J.G. Raftery [1]. The concept of local congruence regularity was introduced in [3]. A common generalization of congruence regularity and local congruence regularity was given in [6] under the name "dual congruence regularity with...
Some modifications of the congruence extension property
Some monounary algebras with EKP
An algebra is said to have the endomorphism kernel property (EKP) if every congruence on is the kernel of some endomorphism of . Three classes of monounary algebras are dealt with. For these classes, all monounary algebras with EKP are described.
Some old and new problems in the independence theory
Some properties of residuated lattices
We investigate some (universal algebraic) properties of residuated lattices—algebras which play the role of structures of truth values of various systems of fuzzy logic.
Some properties of the weak subalgebra lattice of a partial algebra of a fixed type
We investigate, using results from [[p3]], when a given lattice is isomorphic to the weak subalgebra lattice of a partial algebra of a fixed type. First, we reduce this problem to the question when hyperedges of a hypergraph can be directed to a form of directed hypergraph of a fixed type. Secondly, we show that it is enough to consider some special hypergraphs. Finally, translating these results onto the lattice language, we obtain necessary conditions for our algebraic problem, and also, we completely...
Some results on congruences on semihypergroups.
Special congruence triples for a regular semigroup.
Strong endomorphism kernel property for finite Brouwerian semilattices and relative Stone algebras
We show that all finite Brouwerian semilattices have strong endomorphism kernel property (SEKP), give a new proof that all finite relative Stone algebras have SEKP and also fully characterize dual generalized Boolean algebras which possess SEKP.
Strong endomorphism kernel property for monounary algebras
All monounary algebras which have strong endomorphism kernel property are described.
Strong P-congruences on P-regular semigroups.
Strong regular varieties of partial algebras I
Subalgebra lattices of completely simple semigroups.
Subalgebra modular, distributive and boolean varieties of semigroups
Subalgebras and homomorphic images of algebras having the CEP and the WCIP
In the present paper we consider algebras satisfying both the congruence extension property (briefly the CEP) and the weak congruence intersection property (WCIP for short). We prove that subalgebras of such algebras have these properties. We deduce that a lattice has the CEP and the WCIP if and only if it is a two-element chain. We also show that the class of all congruence modular algebras with the WCIP is closed under the formation of homomorphic images.