Schreier-Zassenhaus theorem for algebras. I
Schreier-Zassenhaus theorem for algebras. II
Semigroups and their lattice of congruences II.
Semigroups and their subsemigroup lattices.
Semigroups for which the continuum congruences form finite chains.
Semigroups of transformations restricted by an equivalence
Suppose σ is an equivalence on a set X and let E(X, σ) denote the semigroup (under composition) of all α: X → X such that σ ⊆ α ∘ α −1. Here we characterise Green’s relations and ideals in E(X, σ). This is analogous to recent work by Sullivan on K(V, W), the semigroup (under composition) of all linear transformations β of a vector space V such that W ⊆ ker β, where W is a fixed subspace of V.
Semigroups with A-semidistributive subsemigroup lattices.
Semilattice decomposition of semigroups.
Semilattices of finite arithmetical algebras
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...