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CHARACTIZATION THEOREMS FOR A COMPLETELY DISTRIBUTIVE LATTICE BEING A COMPLETE RING OF SETS

Yuqi Zhang

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Abstract

By using the subdirect product representation theorem for completely distributive lattices of Raney G N,the following results are proved.A completely distributive lattice L is a complete ring of sets??L is a relatively atomic lattice.A completely distributive lattice L is a complete ring of sets??con c(L) is isomorphic to a power set lattice,where con c(L) is the lattice of all complete congruences of L.

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By using the subdirect product representation theorem for completely distributive lattices of Raney G N,the following results are proved.A completely distributive lattice L is a complete ring of sets??L is a relatively atomic lattice.A completely distributive lattice L is a complete ring of sets??con c(L) is isomorphic to a power set lattice,where con c(L) is the lattice of all complete congruences of L.

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Available abstract

By using the subdirect product representation theorem for completely distributive lattices of Raney G N,the following results are proved.A completely distributive lattice L is a complete ring of sets??L is a relatively atomic lattice.A completely distributive lattice L is a complete ring of sets??con c(L) is isomorphic to a power set lattice,where con c(L) is the lattice of all complete congruences of L.

Key concepts: Distributive lattice, Distributive property, Congruence lattice problem, Map of lattices, Lattice (music), Mathematics, Combinatorics, Congruence relation

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