Boolean代数族模素强滤子约化直积可分配的特征性质

The Distributive Characteristic,Property for the Direct Product of a Family of Boolean Algebra Reduced by Mod a Prime and Strong Filter

本文构造一类Ｂｏｏｌｅａｎ代数──Ｂｏｏｌｅａｎ代数族｛Ｂ＿ｔ｝＿ｔ∈Ｔ模素强滤子Ｆ的约化直积Ｒ／Ｆ，证明：Ｐ／Ｆ是可分配的，充分必要｛ｔ：Ｂ＿ｔ是完备原子Ｂｏｏｌｅａｎ代数｝∈Ｆ①．

In this paper a class of Boolean algebra-the direct product P / F of a family {B_t}_t∈T,Boolcan algebra B_t reduced by mod a prime and strong filter F is constructed; We prove (P / P is distributive) if T ({t: B_t is complete and atomic}∈ F).