Regular coverings in filter and ideal lattices

Details Regular coverings in filter and ideal lattices Regular coverings in filter and ideal lattices

2000-05-13

arxiv.org/abs/math/0005131v3

Mathematics

Rings and Algebras

24 pages; version 2: improved results and improved exposition; version 3: minor editorial corrections

Scientific paper

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.

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