2000/05/13 by William H. Rowan, Rowan, William H.
Computer Science · Mathematics · #03F03 (Secondary) #06C99 (Primary) #06D99 #Advanced Algebra and Logic #FOS: Mathematics #Logic, Reasoning, and Knowledge #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic #math.RA #msc:03F03 #msc:06C99 #msc:06D99
paper · pdf · doi:10.48550/arxiv.math/0005131
24 pages; version 2: improved results and improved exposition; version 3: minor editorial corrections
openalex publication_date 2000/05/13 · arxiv created 2002/04/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Dedekind-Birkhoff theorem for finite-height modular lattices has previously been generalized to complete modular lattices using the theory of regular coverings. In this paper, we investigate regular coverings in lattices of filters and lattices of ideals, and the regularization strategy--embedding the lattice into its lattice of filters or lattice of ideals, thereby possibly converting a covering which is not regular into a covering which is regular. One application of the theory is a generalization of the notion of chief factors, and of the Jordan-Holder Theorem, to cases where the modular lattice in question is of infinite height. Another application is a formalization of the notion of the steps in the proof of a theorem.