摘要
对于双重Stone代数L,以P(L)表示L的全体素理想组成的集,Con(L)表示L的同余关系格,XP(L)表示P(L)的幂集格的对偶格。本文用P(L)的子集刻划了双重Stone代数L的每一个同余关系,由此给出了双重Stone代数L关于次直不可约双重Stone代数的次直积表示和双重Stone代数的次直不可约类,并证明了Con(L)可以嵌入到XP(L)中。
For a double Stone algebra L,let P(L) denote the set of all prime ideals of L,let Con(L) be congruence lattice of L,and let X(P(L)) be the dual lattice of the power set of P(L).In this paper,any congruence relations of double L is Characterized by the subsets of P(L),by it we given the subdirect product representation of double Stone algebra L for subdirectly irreducible double stone algebra and subdirectly irreducible class of double Stone algebra.We have also proved that Con(L) can embe into the lattice X(P(L)).
