摘要
得到了如下结果: ①完备集环L是Stone代数当且仅当L的每个完备素滤子仅包含在L 的一个极大滤子中; ②完备集环 L 是 Stone 代数当且仅当 L 是直积不可约 Stone 代数的直积; ③完备集环 L 是Lukasiewicz三值代数当且仅当L同构到一个幂集格.
In this paper,the following results are obtained: ① A complete ring of sets L is a Stone algebra iff every vompletely prime filter of L is exactly contained in a maximal filter. ② A complete ring of sets L is a Stone algebra iff L is the Cartesian product of product-irreducible Stone algebras. ③ A complete ring of sets L is a Lukasiewicz trivalent algebra iff L is isomorphic to a power set lattice.
出处
《内蒙古师范大学学报（自然科学汉文版）》
CAS
2005年第1期19-22,共4页
Journal of Inner Mongolia Normal University(Natural Science Edition)
关键词
完备集环
STONE代数
不可约
直积
滤子
同构
幂集
complete rings of sets
Stone algebras
completely prime filters
product-irreducible Stone algebras
Lukasiewicz trivalent algebras
power set lattices
