Some embedding theorems.
Some examples of primitive lattices
Some finite congruence lattices, I
Some Maximal Closed Classes of Operations on Infinite Sets.
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 pseudovariety joins involving the pseudovariety of finite groups.
Some quasi-ordered classes of finite commutative semigroups.
Some regular quasivarieties of commutative binary modes
Irregular (quasi)varieties of groupoids are (quasi)varieties that do not contain semilattices. The regularization of a (strongly) irregular variety of groupoids is the smallest variety containing and the variety of semilattices. Its quasiregularization is the smallest quasivariety containing and . In an earlier paper the authors described the lattice of quasivarieties of cancellative commutative binary modes, i.e. idempotent commutative and entropic (or medial) groupoids. They are all irregular...
Some relations on the lattice of varieties of completely regular semigroups
On the lattice of varieties of completely regular semigroups considered as algebras with the binary multiplication and unary inversion within maximal subgroups, we study the relations , , , , , , and . Here is the kernel relation, is the trace relation, and are the left and the right trace relations, respectively, for , is the core relation and is the local relation. We give an alternative definition for each of these relations of the form for some subclasses of ....
Some remarks on distributive groupoids
Some results on congruences on semihypergroups.
Some results on the dot-depth hierarchy.
Some subdirectly irreducible idem-potent semigroups.
Spaces and equations
It is proved, for various spaces A, such as a surface of genus 2, a figure-eight, or a sphere of dimension ≠ 1,3,7, and for any set Σ of equations, that Σ cannot be modeled by continuous operations on A unless Σ is undemanding (a form of triviality that is defined in the paper).
Span in incidence structures of independent sets defined on projective space