二元交换算子间的弱支配关系  

Weak dominance relation between binary commutative operators

作　　者：张丽珠 薄其高 李钢 ZHANG Li-zhu;BO Qi-gao;LI Gang(School of Mathematics and Statistics,Qilu University of Technology(Shandong Academy of Sciences),Jinan 250353,China)

机构地区：[1]齐鲁工业大学(山东省科学院)数学与统计学院,山东济南250353

出　　处：《齐鲁工业大学学报》2022年第6期61-67,共7页Journal of Qilu University of Technology

基　　金：国家自然科学基金(61977040);山东省自然科学基金(ZR2019MF055)。

摘　　要：作为二元算子间支配关系的推广,弱支配关系在文献中被引入。主要讨论了二元交换算子间的弱支配关系。首先给出弱支配关系的一些性质,证明了在对偶与同构背景下弱支配关系仍然成立;其次,说明了二元交换算子的单位元、吸收元对弱支配关系的影响;最后,给出了三角模、三角余模、可表示一致模之间的弱支配关系相关结论。The concept of weak dominance as a generalization of the dominance relation between binary operators was introduced in literature.The weak dominance relation is mainly discussed between binary commutative operators.Firstly,some properties of the weak dominance relation are given and it is shown that the weak dominance relation still holds under duality and isomorphism.Secondly,the influence of the neutral element and absorbing element of binary commutative operator is illustrated on the weak dominance relation.Finally,some results are presented about the weak dominance relations between triangular norms,triangular conorms and representable uninorms.

关 键 词：二元交换算子 弱支配关系 同构 三角模 一致模 

分 类 号：O159[理学—数学]