On finite retract lattices of monounary algebras
Danica Jakubı́ková-Studenovská, Jozef Pócs · Mathematica Slovaca · 2012
Abstract For a monounary algebra (A, f) we denote R ∅(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 R ∅(A, f) is finite, then this lattice contains no diamond. Next distributivity of R ∅(A, f) is studied. We find a representation of a certain class of finite distributive lattices as retract lattices of monounary algebras.