并素元有限生成格的弱直积分解

本文建立了并素元有限生成格的弱直积分解,并给出一个解决并素元生成的完全Heyting代数的直积分解问题的新方法;作为弱直积分解的应用,证明了并素元有限生成的完全Heyting代数必然同构于有限个既约的完全Heyting代数的直积,证明了并素元有限生成格是Boole代数的充要条件是它同构于某有限集的幂集格.

Weak Direct Product Decompositions of Lattices Generated Finite-Wisely by co-Primes

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.