素内部算子和素闭包算子与伴随的关系  

Some relations between prime inner operators,prime closure operators and connections

作　　者：徐款款 卢涛[1] Xu Kuankuan;Lu Tao(School of Mathematical Science,Huaibei Normal University,Huaibei 235000,Anhui,China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《江苏师范大学学报（自然科学版）》2018年第3期57-58,68,共3页Journal of Jiangsu Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11571175);安徽省高校自然科学研究重点项目(KJ2016A635)

摘　　要：研究了素内部算子和素闭包算子与伴随的关系,得到了几个主要结论:1)若f是素内部算子,g是素闭包算子,且f,g保序,则(f,g)成为伴随的充分条件是f和g的不动点之集相同;2)在一定条件下,若(f,g)是伴随,则fg是素内部算子,gf是素闭包算子.Some relations between prime inner operators, prime closure operators and Galois connections have been studied. Some main conclusions about the relations of them are obtained： 1） the sufficient condition for （f,g） to be a Galois connection, when f is a prime inner operator, g is a prime closure operator, is that f and g have the same fixed point sets; 2） under certain conditions, if （f, g） is Galois connection, then gf is a prime closure operator and fg is a prime inner operator.

关 键 词：素内部算子 素闭包算子 伴随 

分 类 号：O153.1[理学—数学] O189.1[理学—基础数学]