Sections in orthomodular structures of decompositions
Quantum Algebra
2013-11-13 v1
Abstract
There is a family of constructions to produce orthomodular structures from modular lattices, lattices that are M and M*-symmetric, relation algebras, the idempotents of a ring, the direct product decompositions of a set or group or topological space, and from the binary direct product decompositions of an object in a suitable type of category. We show that an interval [0, a] of such an orthomodular structure constructed from A is again an orthomodular structure constructed from some B built from A. When A is a modular lattice, this B is an interval of A, and when A is an object in a category, this B is a factor of A.
Cite
@article{arxiv.1311.2822,
title = {Sections in orthomodular structures of decompositions},
author = {John Harding and Taewon Yang},
journal= {arXiv preprint arXiv:1311.2822},
year = {2013}
}