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- W2750960094 abstract "Congruence lattices of semiprime algebras from semi--degenerate congruence--modular varieties fulfill the equivalences from B. A. Davey`s well--known characterization theorem for $m$--Stone bounded distributive lattices, moreover, changing the cardinalities in those equivalent conditions does not change their validity. I prove this by transferring Davey`s Theorem from bounded distributive lattices to such congruence lattices through a certain lattice morphism and using the fact that the codomain of that morphism is a frame. Furthermore, these equivalent conditions are preserved by finite direct products of such algebras, and similar equivalences are fulfilled by the elements of semiprime commutative unitary rings and, dualized, by the elements of complete residuated lattices." @default.
- W2750960094 created "2017-09-15" @default.
- W2750960094 creator A5006529371 @default.
- W2750960094 date "2017-09-03" @default.
- W2750960094 modified "2023-10-18" @default.
- W2750960094 title "Transferring Davey`s Theorem on Annihilators in Bounded Distributive Lattices to Modular Congruence Lattices and Rings" @default.
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