摘要
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．
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.
关键词
并素元有限生成格
弱直积分解
完全Heyting代数
lattice generated finite-wisely by co-primes
weak direct product decomposition
complete Heyting algebra
Boolean algebra.
