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A property of the solvable radical in finitely decidable varieties

Paweł M. Idziak, Matthew Valeriote (2001)

Fundamenta Mathematicae

It is shown that in a finitely decidable equational class, the solvable radical of any finite subdirectly irreducible member is comparable to all congruences of the irreducible if the type of the monolith is 2. In the type 1 case we establish that the centralizer of the monolith is strongly solvable.

A scheme for congruence semidistributivity

Ivan Chajda, Eszter K. Horváth (2003)

Discussiones Mathematicae - General Algebra and Applications

A diagrammatic statement is developed for the generalized semidistributive law in case of single algebras assuming that their congruences are permutable. Without permutable congruences, a diagrammatic statement is developed for the ∧-semidistributive law.

An application of commutator theory to incidence algebras.

Paolo Lipparini (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Usando la teoria del commutatore in algebra universale, si dimostra che una larga classe di algebre di incidenza sono polinomialmente equivalenti a moduli su anelli con divisione.

Commutative directoids with sectionally antitone bijections

Ivan Chajda, Miroslav Kolařík, Sándor Radeleczki (2008)

Discussiones Mathematicae - General Algebra and Applications

We study commutative directoids with a greatest element, which can be equipped with antitone bijections in every principal filter. These can be axiomatized as algebras with two binary operations satisfying four identities. A minimal subvariety of this variety is described.

Compatible Idempotent Terms in Universal Algebra

Ivan Chajda, Antonio Ledda, Francesco Paoli (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In universal algebra, we oftentimes encounter varieties that are not especially well-behaved from any point of view, but are such that all their members have a “well-behaved core”, i.e. subalgebras or quotients with satisfactory properties. Of special interest is the case in which this “core” is a retract determined by an idempotent endomorphism that is uniformly term definable (through a unary term t ( x ) ) in every member of the given variety. Here, we try to give a unified account of this phenomenon....

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