Some properties of retract lattices of monounary algebras |
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Authors: | Danica Jakubíková-Studenovská Jozef Pócs |
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Affiliation: | 1.Institute of Mathematics,P. J. ?afárik University,Ko?ice,Slovakia;2.Mathematical Institute,Slovak Academy of Sciences,Ko?ice,Slovakia |
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Abstract: | Necessary and sufficient conditions for a connected monounary algebra (A, f), under which the lattice R ∅(A, f) of all retracts of (A, f) (together with ∅) is algebraic, are proved. Simultaneously, all connected monounary algebras in which each retract is a union of completely join-irreducible elements of R ∅(A, f) are characterized. Further, there are described all connected monounary algebras (A, f) such that the lattice R ∅(A, f) is complemented. In this case R ∅(A, f) forms a boolean lattice. |
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