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Epimorphisms between finite MV-algebras

Aldo V. Figallo, Marina B. Lattanzi (2017)

Mathematica Bohemica

MV-algebras were introduced by Chang to prove the completeness of the infinite-valued Łukasiewicz propositional calculus. Recently, algebraic theory of MV-algebras has been intensively studied. Wajsberg algebras are just a reformulation of Chang MV-algebras where implication is used instead of disjunction. Using these equivalence, in this paper we provide conditions for the existence of an epimorphism between two finite MV-algebras A and B . Specifically, we define the mv-functions with domain in...

Equation f ( p ( x ) ) = q ( f ( x ) ) for given real functions p , q

Oldřich Kopeček (2012)

Czechoslovak Mathematical Journal

We investigate functional equations f ( p ( x ) ) = q ( f ( x ) ) where p and q are given real functions defined on the set ℝ of all real numbers. For these investigations, we can use methods for constructions of homomorphisms of mono-unary algebras. Our considerations will be confined to functions p , q which are strictly increasing and continuous on ℝ . In this case, there is a simple characterization for the existence of a solution of the above equation. First, we give such a characterization. Further, we present a construction...

Equational bases for weak monounary varieties

Grzegorz Bińczak (2002)

Discussiones Mathematicae - General Algebra and Applications

It is well-known that every monounary variety of total algebras has one-element equational basis (see [5]). In my paper I prove that every monounary weak variety has at most 3-element equational basis. I give an example of monounary weak variety having 3-element equational basis, which has no 2-element equational basis.

Equimorphy in varieties of distributive double p -algebras

Václav Koubek, Jiří Sichler (1998)

Czechoslovak Mathematical Journal

Any finitely generated regular variety 𝕍 of distributive double p -algebras is finitely determined, meaning that for some finite cardinal n ( 𝕍 ) , any subclass S ⊆ 𝕍 of algebras with isomorphic endomorphism monoids has fewer than n ( 𝕍 ) pairwise non-isomorphic members. This result follows from our structural characterization of those finitely generated almost regular varieties which are finitely determined. We conjecture that any finitely generated, finitely determined variety of distributive double p -algebras...

Equimorphy in varieties of double Heyting algebras

V. Koubek, J. Sichler (1998)

Colloquium Mathematicae

We show that any finitely generated variety V of double Heyting algebras is finitely determined, meaning that for some finite cardinal n(V), any class 𝒮 ⊆ V consisting of algebras with pairwise isomorphic endomorphism monoids has fewer than n(V) pairwise non-isomorphic members. This result complements the earlier established fact of categorical universality of the variety of all double Heyting algebras, and contrasts with categorical results concerning finitely generated varieties of distributive...

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