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Displaying similar documents to “Subalgebra extensions of partial monounary algebras”

On ideal extensions of partial monounary algebras

Danica Jakubíková-Studenovská (2008)

Czechoslovak Mathematical Journal

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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 ) .

Equation f ( p ( x ) ) = q ( f ( x ) ) for given real functions p , q

Oldřich Kopeček (2012)

Czechoslovak Mathematical Journal

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We investigate functional equations f ( p ( x ) ) = q ( f ( x ) ) where p and q are given real functions defined on the set of all real numbers. For these investigations, we can use methods for constructions of homomorphisms of mono-unary algebras. Our considerations will be confined to functions p , q which are strictly increasing and continuous on . In this case, there is a simple characterization for the existence of a solution of the above equation. First, we give such a characterization. Further, we present...