Hoop residuation algebras are the {→, 1}-subreducts of hoops; they include Hilbert algebras and the {→, 1}-reducts of MV-algebras (also known as Wajsberg algebras). The paper investigates the structure and cardinality of finitely generated algebras in varieties of kpotent hoop residuation algebras. The assumption of k-potency guarantees local finiteness of the varieties considered. It is shown ...

The study of essential and strongly essential variables in functions defined on finite sets is a part of k-valued logic. We extend the main definitions from functions to terms. This allows us to apply concepts and results of Universal Algebra. On the basis of the concept of a separable set of variables in a term we introduce a new notion of complexity of terms, algebras and varieties and give e...

The elementary result of Variety theory is Eilenberg’s Variety theorem which was motivated by characterizations of several families of string languages by syntactic monoids or semigroups, such as Schützenberger’s theorem connecting star-free languages and aperiodic monoids. Eilenberg’s theorem has been extended in various directions. For example, Thérien involved varieties of congruences on fre...

1. p-centers 1 1.1. Notation 1 1.2. Frobenius twist for symplectic varieties 1 1.3. Differential operators 2 1.4. Universal enveloping algebras 2 2. Classical Hamiltonian reduction 2 2.1. GIT in positive characteristic 2 2.2. Frobenius kernel 3 2.3. Hamiltonian actions and reduction 4 3. Frobenius constant quantizations 4 3.1. Definition 4 3.2. Quantum Hamiltonian reduction 5 4. Quantization of...

We show that for finite n ≥ 3, every first-order axiomatisation of the varieties of representable n-dimensional cylindric algebras, diagonal-free cylindric algebras, polyadic algebras, and polyadic equality algebras contains an infinite number of non-canonical formulas. We also show that the class of structures for each of these varieties is non-elementary. The proofs employ algebras derived fr...

We prove that all semisimple varieties of FLew-algebras are discriminator varieties. A characterisation of discriminator and EDPC varieties of FLew-algebras follows. It matches exactly a natural classification of logics over FLew proposed by H. Ono.

The theory of abelian categories proved very useful, providing an ax-iomatic framework for homology and cohomology of modules over a ring (in particular, abelian groups) [5]. A similar framework has been lacking for non-abelian (co)homology, the subject of which includes the categories of groups and Lie algebras etc. The point of my thesis is that semi-abelian categories (in the sense of Janeli...

In [8], P. Jones characterized the regular varieties of semigroups which are congruence semimodular and he partially solved the problem of characterizing the non-regular, congruence semimodular (CSM) varieties of semigroups. For regular varieties his characterization was an equational one, so necessarily a part of his argument was semigroup-theoretic. But some of his argument involved only cong...

The purpose of the present paper is to show that: Eilenberg–type correspondences = Birkhoff’s theorem for (finite) algebras + duality. We consider algebras for a monad T on a category D and we study (pseudo)varieties of T– algebras. Pseudovarieties of algebras are also known in the literature as varieties of finitealgebras. Two well–known theorems that characterize varieties and pseudovarie...