Regular Coverings in Filter and Ideal Lattices
نویسنده
چکیده
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.
منابع مشابه
Semi-G-filters, Stonean filters, MTL-filters, divisible filters, BL-filters and regular filters in residuated lattices
At present, the filter theory of $BL$textit{-}algebras has been widelystudied, and some important results have been published (see for examplecite{4}, cite{5}, cite{xi}, cite{6}, cite{7}). In other works such ascite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory inthe more general setting of residuated lattices is done, generalizing thatfor $BL$textit{-}algebras. Note that fil...
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