软代数的Stone定理  

STONE THEOREM FOR SOFT ALGEBRA

作　　者：郑延履[1] 

机构地区：[1]武汉大学数学系

出　　处：《武汉大学学报（自然科学版）》1994年第3期29-33,共5页Journal of Wuhan University(Natural Science Edition)

基　　金：国家自然科学基金

摘　　要：对于每一个正规软代数Ｆ，对应有一个准Ｂｏｏｌｅ环Ｆ．反之，每一个准Ｂｏｏｌｅ环Ｒ，对应有一个正规软代数Ｒ，且有＝Ｆ，＝Ｒ．M. H. Stone has shown that equivalence of Boolean algebras and Boolean rings. We have shown theorem:1) Let F= (F, ∨, ∧,', 0, 1) be a normal soft algebra. Define F to be the algebra (F,+,·,0, 1 ),where a+b= (a ∨ b) ∧ (a'∨b' ),a· b=a ∧ b. Then F is a quasi-Boolean ring.2) Let R= (R, +,·, 0, 1 ) be a quasi-Boolean ring,Define R to be the algebra(R, ∨,∧,', 0,1 ) where a∨ b= (a+ 1 ) (b+ 1 ) + 1,a ∧ b=a· b,a'=a+ 1. Then R is a normal soft algebra.3) Given F and R as abore we have F=F,R=R.

关 键 词：软代数 准布尔环 Stone定理 

分 类 号：O153.1[理学—数学]