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Weak direct product decompositions of lattices generated finite-wisely by co-primes. (Chinese. English summary) Zbl 0957.06011

Summary: We establish the weak direct product decompositions of lattices generated finite-wisely by co-primes, and solve the problem of direct product decompositions of complete Heyting algebras generated by co-primes in a new way. As an applications, we prove that complete Heyting algebras generated finite-wisely by co-primes are isomorphic to the direct product of finitely many irreducible complete Heyting algebras, and prove that a lattice generated finite-wisely by co-primes is a Boolean algebra if and only if it is isomorphic to the power set lattice of a finite set.

MSC:

06D20 Heyting algebras (lattice-theoretic aspects)
06B05 Structure theory of lattices
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