The reflectiveness of covering morphisms in algebra and geometry.
The strong amalgamation property
The varieties of languages corresponding to the varieties of finite band monoids.
The weak extension property and finite axiomatizability for quasivarieties
We define and compare a selection of congruence properties of quasivarieties, including the relative congruence meet semi-distributivity, RSD(∧), and the weak extension property, WEP. We prove that if 𝒦 ⊆ ℒ ⊆ ℒ' are quasivarieties of finite signature, and ℒ' is finitely generated while 𝒦 ⊨ WEP, then 𝒦 is finitely axiomatizable relative to ℒ. We prove for any quasivariety 𝒦 that 𝒦 ⊨ RSD(∧) iff 𝒦 has pseudo-complemented congruence lattices and 𝒦 ⊨ WEP. Applying these results and other results...
Transferral of entailment in duality theory: dualisability
A number of new results that say how to transfer the entailment relation between two different finite generators of a quasi-variety of algebras is presented. As their consequence, a well-known result saying that dualisability of a quasi-variety is independent of the generating algebra is derived. The transferral of endodualisability is also considered and the results are illustrated by examples.
Transferral of entailment in duality theory II: strong dualisability
Results saying how to transfer the entailment in certain minimal and maximal ways and how to transfer strong dualisability between two different finite generators of a quasi-variety of algebras are presented. A new proof for a well-known result in the theory of natural dualities which says that strong dualisability of a quasi-variety is independent of the generating algebra is derived.
Unequivocal linearly ordered groups
Uniqueness of improper operations
Valuations of structures
Varieties generated by two-element majority algebras and their equivalences
Varieties of finite categories
Various remarks on quasi-universal model classes.
Weak alg-universality and -universality of semigroup quasivarieties
In an earlier paper, the authors showed that standard semigroups , and play an important role in the classification of weaker versions of alg-universality of semigroup varieties. This paper shows that quasivarieties generated by and are neither relatively alg-universal nor -universal, while there do exist finite semigroups and generating the same semigroup variety as and respectively and the quasivarieties generated by and/or are quasivar-relatively -alg-universal and -universal...
Аксиоматизируемость и модельная полнота класса регулярных полигонов.
Аксиоматизируемость и полнота некоторых классов -полигонов.
Аксиоматизируемость одной проекции универсально аксиомтизируемого класса алгебраических систем
Аксиоматический ранг квазимногообразия правоупорядочиваемых групп.
Аксиоматический ранг квазимногообразия, содержащего свободную разрешимую группу
Алгебра Грецера и S-системы квазигрупп
Алгебраические точечные решетки квазимногообразий.