On the permanence properties of interval homogeneous orthomodular lattices
Anna De Simone, Mirko Navara · Czech digital mathematics library · 2004
An orthomodular lattice L is said to be interval homogeneous if it is a -complete and satisfies the following property: Whenever L is isomorphic to an interval [a, b] in L, then L is isomorphic to each interval [c, d] D [a, b].This class was introduced in the effort to determine the orthomodular lattices which satisfy the Cantor-Bernstein theorem.In this paper we carry on the investigation of this important class.We investigate permanence properties of this class with respect to the formation of substructures and a -epimorphic images.We show that there are also fairly complex examples of interval homogeneous orthomodular lattices.In fact, we show as a main result that every a -complete orthomodular lattice (abbreviated a-OML) can be embedded into an interval homogeneous orthomodular lattice.In a somewhat dual sense, we find that each cr-OML is a a -epimorphic image of an interval homogeneous orthomodular lattice.