On finite retract lattices of monounary algebras

Rok, strany: 2012, 187 - 200

For a monounary algebra $(A,f)$ we denote $\mathbf{R}^\emptyset(A,f)$ the system of all retracts (together with the empty set) of $(A,f)$ ordered by inclusion. This system forms a lattice. We prove that if $(A,f)$ is a connected monounary algebra and $\mathbf{R}^\emptyset(A,f)$ is finite, then this lattice contains no diamond. Next distributivity of $\mathbf{R}^\emptyset(A,f)$ is studied. We find a representation of a certain class of finite distributive lattices as retract lattices of monounary algebras.

ISO 690:

Studenovská, D., Pócs, J. 2012. On finite retract lattices of monounary algebras. In Mathematica Slovaca, vol. 62, no.2, pp. 187-200. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0003-3

APA:

Studenovská, D., Pócs, J. (2012). On finite retract lattices of monounary algebras. Mathematica Slovaca, 62(2), 187-200. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0003-3