Jin, Chenhui Weak direct product decompositions of lattices generated finite-wisely by co-primes. (Chinese. English summary) Zbl 0957.06011 J. Math. Res. Expo. 20, No. 2, 283-286 (2000). 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 Keywords:weak direct product decompositions; complete Heyting algebras; co-primes; Boolean algebra PDFBibTeX XMLCite \textit{C. Jin}, J. Math. Res. Expo. 20, No. 2, 283--286 (2000; Zbl 0957.06011)