Shift-automorphism methods for inherently nonfinitely based varieties of algebras
Small idempotent clones. I
G. Grätzer and A. Kisielewicz devoted one section of their survey paper concerning -sequences and free spectra of algebras to the topic “Small idempotent clones” (see Section 6 of [18]). Many authors, e.g., [8], [14, 15], [22], [25] and [29, 30] were interested in -sequences of idempotent algebras with small rates of growth. In this paper we continue this topic and characterize all idempotent groupoids with (see Section 7). Such groupoids appear in many papers see, e.g. [1], [4], [21], [26,...
Solid varieties of semigroups.
Solvability of equations in varieties of universal algebras.
Some decidable theories with finitely many covers which are decidable and algorithmically found
In any recursive algebraic language, I find an interval of the lattice of equational theories, every element of which has finitely many covers. With every finite set of equations of this language, an equational theory of this interval is associated, which is decidable with decidable covers that can be algorithmically found. If the language is finite, both this theory and its covers are finitely based. Also, for every finite language and for every natural number n, I construct a finitely based decidable...
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 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.
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).
Strong regular varieties of partial algebras I
Subcoherent algebras
Subdirectly irreducible groupoids in some varieties
Super-De Morgan functions and free De Morgan quasilattices
A De Morgan quasilattice is an algebra satisfying hyperidentities of the variety of De Morgan algebras (lattices). In this paper we give a functional representation of the free n-generated De Morgan quasilattice with two binary and one unary operations. Namely, we define the concept of super-De Morgan function and prove that the free De Morgan quasilattice with two binary and one unary operations on nfree generators is isomorphic to the De Morgan quasilattice of super-De Morgan functions of nvariables....
Sur quelques problèmes de plongement en algèbre
Sur quelques problèmes de plongements en algèbre