Informácia o dokumente



In: Mathematica Slovaca, vol. 54, no. 1
Anna De Simone - Mirko Navara

On the permanence properties of interval homogeneous orthomodular lattices

Detaily:

Rok, strany: 2004, 13 - 21

O článku:

An orthomodular lattice $L$ is said to be interval homogeneous if it is $σ$@-complete and satisfies the following property: Whenever $L$ is isomorphic to an interval $[a,b]$ in $L$, then $L$ is isomorphic to each interval $[c,d]\supseteq[a,b]$. 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 $σ$@-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 $σ$@-complete orthomodular lattice (abbreviated $σ$@-OML) can be embedded into an interval homogeneous orthomodular lattice. In a somewhat dual sense, we find that each $σ$@-OML is a $σ$@-epimorphic image of an interval homogeneous orthomodular lattice.

Ako citovať:

ISO 690:
De Simone, A., Navara, M. 2004. On the permanence properties of interval homogeneous orthomodular lattices. In Mathematica Slovaca, vol. 54, no.1, pp. 13-21. 0139-9918.

APA:
De Simone, A., Navara, M. (2004). On the permanence properties of interval homogeneous orthomodular lattices. Mathematica Slovaca, 54(1), 13-21. 0139-9918.