| In this paper, 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 applications, we prove that complete Heyting algebras generated finite-wisely by co-primes are isomorphic to the direct product of finite 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's isomorphic to the power set lattice of a finite set. |
