摘要
文章借助连续格与Domain中的弱素元与way-below关系的定义,通过对偏序集中的闭包算子和内部算子的研究,给出弱素内部算子的定义.讨论闭包算子、内部算子与way-below关系之间的联系,以及弱素内部算子与闭包算子和内部算子之间的关系.将弱素元的定义与格理论中的素理想定义相结合,推出弱素理想的定义,并得到弱素内部算子与弱素理想的相应等价刻画.推广相关文献的有关结论,进一步丰富偏序集中的算子理论.
In this paper,with the definition of weak prime element and the way-below relation in the continuous lattices and Domain theory,based on concentrated closure operator and interior operator of the partial order set research,presents the definition of weak prime interior operator.The relationship between closure operators,interior operators and way-below relation,and the relationship between weak prime interior operator,closure operator and the interior operator.In addition,by combining the definition of weak prime element with the definition of prime ideal in lattice theory is discussed.The definition of weak prime ideal is derived,and the corresponding equivalent characterizations of weak prime interior operator and weak prime ideal are obtained.The literature relevant to the conclusion is promoted,which further enriches the partial order operator theory.
作者
汪鲲
卢涛
WANG Kun;LU Tao(School of Mathematical Sciences,Huaibei Normal University,235000,Huaibei,Anhui,China)
出处
《淮北师范大学学报（自然科学版）》
CAS
2019年第1期1-4,共4页
Journal of Huaibei Normal University：Natural Sciences
基金
国家自然科学基金资助项目(11571175)
关键词
闭包算子
内部算子
弱素元
弱素理想
弱素内部算子
closure operator
interior operator
weak prime element
weak prime ideal
weak prime interior operator
