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The minimal nontrivial endomorphism monoids $M = End Con (A, F)$ of congruence lattices of algebras $(A, F)$ defined on a finite set $A$ are described. They correspond (via the Galois connection $End$ - $Con$ ) to the maximal nontrivial congruence lattices $Con (A, F)$ investigated and characterized by the authors in previous papers. Analogous results are provided for endomorphism monoids of quasiorder lattices $Quord (A, F)$ .

Transferral of entailment in duality theory: dualisability

Maria Joao Gouveia, Miroslav Haviar (2011)

Czechoslovak Mathematical Journal

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

Maria João Gouveia, Miroslav Haviar (2011)

Czechoslovak Mathematical Journal

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.

Transitively acting monoids of local automorphisms of locally finite trees

Jan Chvalina, Ludmila Chvalinová (1983)

Archivum Mathematicum

Turning retractions of an algebra into an algebra.

Mašulović, Dragan (2004)

Novi Sad Journal of Mathematics

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