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Graph homomorphisms of partial monounary algebras. (English) Zbl 1108.08002
A partial monounary algebra is a pair \((V,f)\), where \(V\) is a nonempty set and \(f\) is a partial unary operation defined on \(A\subseteq V\). Partial monounary algebras can be represented by graphs. To each partial monounary algebra \((V,f)\) there correspond two graphs, \(G(V,f)=(V,E)\) and \(G'(V,f)=(V,E')\) such that \(E\) and \(E'\) are binary operations on \(V\) defined by putting \((x,y)\in E\) if and only if \(f(x)=y\), and \((x,y)\in E'\) if and only if \(x\neq y\) and \(f(x)=y\). Therefore the graph \(G(V,f)\) admits loops while \(G'(V,f)\) contains no loops. By means of the strong homomorphism of graphs the notions of a \(G\)-homomorphism and a \(G'\)-homomorphism of partial monounary algebras are introduced and studied in this paper.

08A55 Partial algebras
08A60 Unary algebras
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