Test elements and the Retract Theorem for monounary algebras

Danica Jakubíková-Studenovská; Jozef Pócs

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Displaying similar documents to “Test elements and the Retract Theorem for monounary algebras”

Cardinality of retracts of monounary algebras

Danica Jakubíková-Studenovská, Jozef Pócs (2008)

Czechoslovak Mathematical Journal

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For an uncountable monounary algebra $(A, f)$ with cardinality $κ$ it is proved that $(A, f)$ has exactly $2^{κ}$ retracts. The case when $(A, f)$ is countable is also dealt with.

Representation of connected monounary algebras by means of irreducibles

Danica Jakubíková-Studenovská (2005)

Czechoslovak Mathematical Journal

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The aim of the present paper is to describe all connected monounary algebras for which there exists a representation by means of connected monounary algebras which are retract irreducible in the class $𝒰_{c}$ (or in $𝒰$ ).

Two types of retract irreducibility of connected monounary algebras

Danica Jakubíková-Studenovská (1996)

Mathematica Bohemica

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Let $𝒜$ be a connected monounary algebra. The paper deals with retract irreducibility of $𝒜$ in the class of all connected monounary algebras and in the class of all monounary algebras.