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Representation of connected monounary algebras by means of irreducibles

Danica Jakubíková-Studenovská (2005)

Czechoslovak Mathematical Journal

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 ).

Some monounary algebras with EKP

Emília Halušková (2020)

Mathematica Bohemica

An algebra 𝒜 is said to have the endomorphism kernel property (EKP) if every congruence on 𝒜 is the kernel of some endomorphism of 𝒜 . Three classes of monounary algebras are dealt with. For these classes, all monounary algebras with EKP are described.

Strong retracts of unary algebras

Rozália Sz. Madarász, Dragan Mašulović, Boža Tasić (2001)

Czechoslovak Mathematical Journal

This paper introduces the notion of a strong retract of an algebra and then focuses on strong retracts of unary algebras. We characterize subuniverses of a unary algebra which are carriers of its strong retracts. This characterization enables us to describe the poset of strong retracts of a unary algebra under inclusion. Since this poset is not necessarily a lattice, we give a necessary and sufficient condition for the poset to be a lattice, as well as the full description of the poset.

Subalgebra extensions of partial monounary algebras

Danica Jakubíková-Studenovská (2006)

Czechoslovak Mathematical Journal

For a subalgebra ℬ of a partial monounary algebra 𝒜 we define the quotient partial monounary algebra 𝒜 / ℬ . Let ℬ , 𝒞 be partial monounary algebras. In this paper we give a construction of all partial monounary algebras 𝒜 such that ℬ is a subalgebra of 𝒜 and 𝒞 ≅ 𝒜 / ℬ .

Subdirect products of certain varieties of unary algebras

Miroslav Ćirić, Tatjana Petković, Stojan Bogdanović (2007)

Czechoslovak Mathematical Journal

J. Płonka in [12] noted that one could expect that the regularization ℛ ( K ) of a variety K of unary algebras is a subdirect product of K and the variety D of all discrete algebras (unary semilattices), but is not the case. The purpose of this note is to show that his expectation is fulfilled for those and only those irregular varieties K which are contained in the generalized variety T D i r of the so-called trap-directable algebras.

Test elements and the Retract Theorem for monounary algebras

Danica Jakubíková-Studenovská, Jozef Pócs (2007)

Czechoslovak Mathematical Journal

The term “Retract Theorem” has been applied in literature in connection with group theory. In the present paper we prove that the Retract Theorem is valid (i) for each finite structure, and (ii) for each monounary algebra. On the other hand, we show that this theorem fails to be valid, in general, for algebras of the form 𝒜 = ( A , F ) , where each f ∈ F is unary and card F > 1 .

Currently displaying 81 – 100 of 126