Central envelopes of orthomodular lattices

Rok, strany: 1993, 221 - 227

Suppose that $\{L_α|α\in I\}$ is a collection of orthomodular lattices and suppose that $B$ is a Boolean algebra. An orthomodular lattice $L$ is called a $B$-envelope of $\{L_α|α\in I\}$ if $L$ contains every $L_α(α\in I)$ and if the centre of $L$ equals $B$. We show in this note that every collection of orthomodular lattices has a $B$-envelope for any Boolean algebra $B$. We then ask an analogous question for $σ$-complete and complete orthomodular lattices. In the latter cases we have been able to find only a partial answer (Th. 2 – 4). The results may find applications in the mathematical foundations of quantum theories.

ISO 690:

Pták, P. 1993. Central envelopes of orthomodular lattices. In Tatra Mountains Mathematical Publications, vol. 2, no.1, pp. 221-227. 1210-3195.

APA:

Pták, P. (1993). Central envelopes of orthomodular lattices. Tatra Mountains Mathematical Publications, 2(1), 221-227. 1210-3195.