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Maltsev families of varieties closed under join or Maltsev product
Maltsev families of varieties which are closed under join or Maltsev product are investigated. New Maltsev conditions for congruence...
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Commutative idempotent groupoids and the constraint satisfaction problem
A restatement of the Algebraic Dichotomy Conjecture, due to Maroti and McKenzie, postulates that if a finite algebra A possesses a weak...
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On inverse limits of monounary algebras
We study inverse limits of monounary algebras. All monounary algebras A such that A can arise from A only by an inverse limit construction are...
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Coproducts of distributive lattice-based algebras
This paper presents a systematic study of coproducts. This is carried out principally, but not exclusively, for finitely generated quasivarieties
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Absolute retracts and essential extensions in congruence modular varieties
This paper studies absolute retracts in congruence modular varieties of universal algebras. It is shown that every absolute retract with finite...
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On independent varieties and some related notions
We investigate the relation of independence between varieties, as well as a generalisation of such which we call strict quasi-independence ....
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Boolean-like algebras
Using Vaggione’s concept of central element in a double-pointed algebra, we introduce the notion of Boolean-like variety as a generalisation of...
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The variety of quasi-Stone algebras does not have the amalgamation property
We give an example showing that the variety of quasi-Stone algebras does not have the amalgamation property.
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A note on profinite completions and canonical extensions
J. Harding has proved that the profinite limit of an algebra A in a finitely generated variety of monotone lattice expansions coincides with its...
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Natural extensions and profinite completions of algebras
This paper investigates profinite completions of residually finite algebras, drawing on ideas from the theory of natural dualities. Given a class
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Universality of Categories of Coalgebras
Under GCH, a set functor F does not preserve finite unions of non-empty sets if and only if the category Coalg F of all F -coalgebras is universal....
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Algebraically closed algebras in certain small congruence distributive varieties
In a finitely generated congruence distributive variety satisfying a weak congruence extension property, the algebraically closed algebras are...
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All clones are centralizer clones
We show that any clone without virtual constants is isomorphic to the centralizer clone of a unary universal algebra, and that adding one unary...
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Lifting retracted diagrams with respect to projectable functors
We prove a general categorical theorem that enables us to state that under certain conditions, the range of a functor is large. As an application, we...
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Functional monadic Heyting algebras
We show every monadic Heyting algebra is isomorphic to a functional monadic Heyting algebra. This solves a 1957 problem of Monteiro and Varsavsky...
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Notes on sums of algebras, subdirect products and subdirectly irreducible algebras
The paper shows that certain sums of algebras admit a representation as subdirect products. As a corollary, one obtains a characterization of...