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On invariance of monounary algebras. (English) Zbl 1234.08007
Chajda, I. (ed.) et al., Proceedings of the 79th workshop on general algebra “79. Arbeitstagung Allgemeine Algebra”, 25th conference of young algebraists, Palacký University Olomouc, Olomouc, Czech Republic, February 12–14, 2010. Klagenfurt: Verlag Johannes Heyn (ISBN 978-3-7084-0407-3/pbk). Contributions to General Algebra 19, 113-126 (2010).
An algebra \(A\) is called fully invariant with respect to congruences (quasiorders) if each of its endomorphisms respects all congruences (quasiorders). If \(M\) is a nonempty subset of \(A\) and \(h\) is a mapping of \(A\) onto \(M\) such that \(h\) is an endomorphism of \(A\) and \(h(x)=x\) for every \(x\in M\), then \(h\) is called a retraction endomorphism corresponding to \(M\) (a retraction endomorphism, for short). In the paper, monounary algebras in which each retraction endomorphism respects all congruences (quasiorders) are investigated.
For the entire collection see [Zbl 1201.08001].
08A60 Unary algebras