On a variety of infinite algebras
On algebras and clones.
On connections between the decomposition of an algebra into sums of direct systems of subalgebras
On distributive trices
A triple-semilattice is an algebra with three binary operations, which is a semilattice in respect of each of them. A trice is a triple-semilattice, satisfying so called roundabout absorption laws. In this paper we investigate distributive trices. We prove that the only subdirectly irreducible distributive trices are the trivial one and a two element one. We also discuss finitely generated free distributive trices and prove that a free distributive trice with two generators has 18 elements.
On equations of clones
On extending congruences from partial algebras
On free modes
We prove a theorem describing the equational theory of all modes of a fixed type. We use this result to show that a free mode with at least one basic operation of arity at least three, over a set of cardinality at least two, does not satisfy identities selected by ’A. Szendrei in Identities satisfied by convex linear forms, Algebra Universalis 12 (1981), 103–122, that hold in any subreduct of a semimodule over a commutative semiring. This gives a negative answer to the question raised by A. Romanowska:...
On free Turing algebras
On generalized products preserving compactness.
On multiplication groups of relatively free quasigroups isotopic to Abelian groups
If is a quasigroup that is free in the class of all quasigroups which are isotopic to an Abelian group, then its multiplication group is a Frobenius group. Conversely, if is a Frobenius group, a quasigroup, then has to be isotopic to an Abelian group. If is, in addition, finite, then it must be a central quasigroup (a -quasigroup).
On semidirect and two-sided semidirect products of finite trivial monoids
On some operator defined on equational classes of algebras
On sums in generalized algebraic categories
On the associative Nijenhuis relation.
One More Categorical Model of Universal Algebra.
Orthocomplemented difference lattices with few generators
The algebraic theory of quantum logics overlaps in places with certain areas of cybernetics, notably with the field of artificial intelligence (see, e. g., [19, 20]). Recently an effort has been exercised to advance with logics that possess a symmetric difference ([13, 14]) - with so called orthocomplemented difference lattices (ODLs). This paper further contributes to this effort. In [13] the author constructs an ODL that is not set-representable. This example is quite elaborate. A main result...