Quantic格上的同态定理  

The homomorphism theorem on Quantic lattices

作　　者：王顺钦[1] 赵彬[2] 

机构地区：[1]南阳师范学院数学与统计学院,河南南阳473061 [2]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《陕西师范大学学报（自然科学版）》2009年第3期5-8,12,共5页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10871121);南阳师范学院博士基金资助项目(nynu200749);南阳市科技攻关项目(2008SF604)

摘　　要：研究了Quantic格的内部运算,证明了Quantic格中的二元运算&满足结合律的充分必要条件是对任意的a、b、c∈Q,均有a&b→c=a→(b→c).讨论了商Quantic格与核映射之间的关系,证明了Quantic格上的同态定理:设f:P→Q是满的Quantic格同态,则存在P上的核映射j,使得Pj≌Q.The interior operations of a quantic lattice Q are discussed and it is proved that a sufficient and necessary condition for the binary operation ＆amp; to be associative is a＆amp;b→c=a→（b→c） for all a,b,c∈Q.The relations between quotient quantic lattices and nuclei in a quantic lattice are discussed.At last,a homomorphism theorem is given,which says that if f： P→Q is a surjective homomorphism between quantic lattices,then there is a nucleus j in P such that Pj≌Q.

关 键 词：完备格 Quantic格 同态定理 核映射 

分 类 号：O153.1[理学—数学]