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On 2-homogeneity of monounary algebras

Danica Jakubíková-Studenovská (2003)

Czechoslovak Mathematical Journal

Fraïssé introduced the notion of a k -set-homogeneous relational structure. In the present paper the following classes of monounary algebras are described: 𝒮 h 2 ( S ) , 𝒮 h 2 ( S c ) , 𝒮 h 2 ( P c ) —the class of all algebras which are 2-set-homogeneous with respect to subalgebras, connected subalgebras, connected partial subalgebras, respectively, and ℋ 2 ( S ) , ℋ 2 ( S c ) , ℋ 2 ( P c ) —the class of all algebras which are 2-homogeneous with respect to subalgebras, connected subalgebras, connected partial subalgebras, respectively.

On a representation of monounary algebras

Danica Jakubíková-Studenovská (2005)

Czechoslovak Mathematical Journal

In this note we deal with a question concerning monounary algebras which is analogous to an open problem for partially ordered sets proposed by Duffus and Rival.

On congruences of G -sets

Boris M. Vernikov (1997)

Commentationes Mathematicae Universitatis Carolinae

We describe G -sets whose congruences satisfy some natural lattice or multiplicative restrictions. In particular, we determine G -sets with distributive, arguesian, modular, upper or lower semimodular congruence lattice as well as congruence n -permutable G -sets for n = 2 , 2 . 5 , 3 .

On ideal extensions of partial monounary algebras

Danica Jakubíková-Studenovská (2008)

Czechoslovak Mathematical Journal

In the present paper we introduce the notion of an ideal of a partial monounary algebra. Further, for an ideal ( I , f I ) of a partial monounary algebra ( A , f A ) we define the quotient partial monounary algebra ( A , f A ) / ( I , f I ) . Let ( X , f X ) , ( Y , f Y ) be partial monounary algebras. We describe all partial monounary algebras ( P , f P ) such that ( X , f X ) is an ideal of ( P , f P ) and ( P , f P ) / ( X , f X ) is isomorphic to ( Y , f Y ) .

On some constructions of algebraic objects

Miroslav Novotný (2006)

Czechoslovak Mathematical Journal

Mono-unary algebras may be used to construct homomorphisms, subalgebras, and direct products of algebras of an arbitrary type.

On some non-obvious connections between graphs and unary partial algebras

Konrad Pióro (2000)

Czechoslovak Mathematical Journal

In the present paper we generalize a few algebraic concepts to graphs. Applying this graph language we solve some problems on subalgebra lattices of unary partial algebras. In this paper three such problems are solved, other will be solved in papers [Pió I], [Pió II], [Pió III], [Pió IV]. More precisely, in the present paper first another proof of the following algebraic result from [Bar1] is given: for two unary partial algebras 𝐀 and 𝐁 , their weak subalgebra lattices are isomorphic if and only...

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