On finite lattices which are embeddable in subsemigroup lattices.
On finitely based varieties of algebras
On frame congruences generated by frame tolerances
Nuclei of frame congruences generated by frame tolerances and by lattice congruences are constructed.
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 pseudo-complemented and relatively pseudo-complemented semi-lattices
On free Turing algebras
On full partial quasigroups of finite order and local cardinal maximum codes.
On functions commuting with semigroups of transformations of algebras.
On -lattices
On general algebras
On generalized conditionally commutative semigroups
On generalized products preserving compactness.
On generating large classes of Sheffer functions.
On Grätzer's problem of binary 1-step congruence schemes
On groups in which idempotent reducts form a chain
On hyperplanes and semispaces in max–min convex geometry
The concept of separation by hyperplanes and halfspaces is fundamental for convex geometry and its tropical (max-plus) analogue. However, analogous separation results in max-min convex geometry are based on semispaces. This paper answers the question which semispaces are hyperplanes and when it is possible to “classically” separate by hyperplanes in max-min convex geometry.
On ideal extensions of partial monounary algebras
In the present paper we introduce the notion of an ideal of a partial monounary algebra. Further, for an ideal of a partial monounary algebra we define the quotient partial monounary algebra . Let , be partial monounary algebras. We describe all partial monounary algebras such that is an ideal of and is isomorphic to .
On ideals and congruences in BCC-algebras
We introduce a new concept of ideals in BCC-algebras and describe connections between such ideals and congruences.
On ideals in De Morgan residuated lattices
In this paper, we introduce a new class of residuated lattices called De Morgan residuated lattices, we show that the variety of De Morgan residuated lattices includes important subvarieties of residuated lattices such as Boolean algebras, MV-algebras, BL-algebras, Stonean residuated lattices, MTL-algebras and involution residuated lattices. We investigate specific properties of ideals in De Morgan residuated lattices, we state the prime ideal theorem and the pseudo-complementedness of the ideal...
On ideals in Hilbert algebras