2002/11/15 by Gerhard Dorfer, Dorfer, Gerhard · 1 citation
Computer Science · Mathematics · #06C15 #81P10 #Advanced Algebra and Logic #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:06C15 #msc:81P10
paper · pdf · doi:10.48550/arxiv.math/0211237
9 pages; some typos fixed, minor grammatical changes; to appear in proceedings to QS2002
openalex publication_date 2002/11/15 · arxiv created 2003/04/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We deal with the following question: What is the proper way to introduce symmetric difference in orthomodular lattices? Imposing two natural conditions on this operation, six possibilities remain: the two (commutative) normal forms of the symmetric difference in Boolean algebras and four non-commutative terms. It turns out that in many respects the non-commutative forms, though more complex with espect to the lattice operations, in their properties are much nearer to the symmetric difference in Boolean algebras than the commutative terms. As application we demonstrate the usefullness of non-commutative symmetric differences in the context of congruence relations.