S-超格理想的相关性质  

On the properties of S-hyperlattice ideals

作　　者：刘妮[1] 崔盼盼 LIU Ni;CUI Panpan(School of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710119,Shaanxi,China)

机构地区：[1]陕西师范大学数学与统计学院,陕西西安710119

出　　处：《山东大学学报(理学版)》2025年第2期1-8,共8页Journal of Shandong University(Natural Science)

摘　　要：本文对S-超格理想的性质进行了探究。证明了两个S-超格的S-超格理想的直积是它们直积的S-超格理想,S-超格理想在S-超格满同态下的像和原像仍为S-超格理想,任意S-超格的全体S-超格理想构成一个代数的有顶交结构。举例说明了对于S-超格同余,最小元0所在的同余类一般不是S-超格理想,并给出了它是S-超格理想的一个充分条件,同时对任意S-超格理想,构造了以其为同余类的最大的S-超格同余。In this paper,the properties of S-hyperlattice ideals are explored.It is proved that the direct product of S-hyperlattice ideals of two S-hyperlattices is an S-hyperlattice ideal of their direct product,the homomorphic image and preimage of S-hyperlattice ideal are still S-hyperlattice ideals,the set of all S-hyperlattice ideals of an S-hyperlattice is an algebraic topped meet structure.It is illustrated that for an S-hyperlattice congruence,the congruence class of the smallest element zero is generally not an S-hyperlattice ideal,and a sufficient condition for it to be an S-hyperlattice ideal is given.While for an S-hyperlattice ideal,a maximal Shyperlattice congruence with it as a congruence class is constructed.

关 键 词：超格 S-超格 S-超格理想 S-超格同余 交结构 

分 类 号：O153.1[理学—数学]