偏序集上的素强理想  

Prime strong ideals on posets

作　　者：陈方鑫 姜广浩[1] 唐照勇 Chen Fangxin;Jiang Guanghao;Tang Zhaoyong(School of Mathematics Science,Huaibei Normal University,Huaibei 235000,Anhui,China;Guangling College,Yangzhou University,Yangzhou 225000,Jiangsu,China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000 [2]扬州大学广陵学院,江苏扬州225000

出　　处：《江苏师范大学学报（自然科学版）》2019年第2期41-43,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(11361028);安徽高等学校省级自然科学研究重点项目(Kj2017A378);安徽省高校省级质量工程项目(2017jxtd146);淮北师范大学学位与研究生教育项目(2017jyxm03)

摘　　要：首先,在偏序集上引入并考察素强理想,探讨素强理想、素理想、强理想3者之间的关系;其次,给出强理想与素强理想等价的一个充分条件;最后,得到序同构映射下(素)强理想的像仍是(素)强理想.In this paper, firstly, the concept of prime strong ideal on posets is introduced and examined. The relationships of prime strong ideal, prime ideal, and strong ideal are explored. Secondly, a sufficient condition for equivalence between strong ideals and prime strong ideals is given. Finally, the result that the image of a (prime) strong ideal under an order isomorphic mapping is still a (prime) strong ideal is obtained.

关 键 词：素理想 强理想 素强理想 序同构映射 

分 类 号：O153.1[理学—数学]