2013/11/12 by John Harding, Harding, John, Taewon Yang +1
Computer Science · Mathematics · #06C15 #18B99 #81P10 #Advanced Algebra and Logic #FOS: Mathematics #Logic, Reasoning, and Knowledge #Quantum Algebra (math.QA) #Rough Sets and Fuzzy Logic #math.QA #msc:06C15 #msc:18B99 #msc:81P10
paper · pdf · doi:10.48550/arxiv.1311.2822
arxiv created 2013/11/12 · openalex publication_date 2013/11/12 · arxiv updated 2013/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.