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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.

Equational compactness in infinitary algebras

Bernhard Banaschewski, Evelyn Nelson (1973)

Colloquium Mathematicae

Equational logic and theories in sentential languages

Roman Suszko (1974)

Colloquium Mathematicae

Equational Reformulation Of Formal Theories

Slaviša B. Prešić (1975)

Publications de l'Institut Mathématique

Equationally compact algebras (I)

B. Węglorz (1966)

Fundamenta Mathematicae

Equationally compact algebras II

Jan Mycielski, Czesław Ryll-Nardzewski (1967)

Fundamenta Mathematicae

Equationally compact algebras (III)

B. Węglorz (1967)

Fundamenta Mathematicae

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 $S \subseteq 𝕍$ 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...