Orthocomplemented weak tensor products

Details Orthocomplemented weak tensor products Orthocomplemented weak tensor products

2011-09-08

arxiv.org/abs/1109.1658v1

Algebra Universalis, vol. 64, p. 379-396 (2010)

Mathematics

Logic

arXiv admin note: substantial text overlap with arXiv:math/0304350

Scientific paper

Let L_1 and L_2 be complete atomistic lattices. In a previous paper, we have defined a set S=S(L_1,L_2) of complete atomistic lattices, the elements of which are called weak tensor products of L_1 and L_2. S is defined by means of three axioms, natural regarding the description of some compound systems in quantum logic. It has been proved that S is a complete lattice. The top element of S, denoted by L_1 v L_2, is the tensor product of Fraser whereas the bottom element, denoted by L_1 ^ L_2, is the box product of Graetzer and Wehrung. With some additional hypotheses on L_1 and L_2 (true for instance if L_1 and L_2 are moreover orthomodular with the covering property) we prove that S is a singleton if and only if L_1 or L_2 is distributive, if and only if L_1 v L_2 has the covering property. Our main result reads: L in S admits an orthocomplementation if and only if L=L_1 ^ L_2. At the end, we construct an example in S which has the covering property.

Affiliated with

Also associated with

No associations

Rating

Orthocomplemented weak tensor products does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Orthocomplemented weak tensor products, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Orthocomplemented weak tensor products will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-474974