矩形Clifford双半环的性质与结构  

Property and structure of rectangular Clifford bi-semirings

作　　者：魏孟君 李刚 WEI Meng-jun;LI Gang(School of Mathematics and Statistics,Shandong Normal University,Jinan 250358,Shandong,China)

机构地区：[1]山东师范大学数学与统计学院,山东济南250358

出　　处：《山东大学学报（理学版）》2022年第10期16-20,27,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11601288)。

摘　　要：利用双半环的分配格和带双半环,将左双环和左Clifford双半环进行推广,得到了矩形双环和矩形Clifford双半环的概念。给出了矩形双环和矩形Clifford双半环的刻画,得到了矩形Clifford双半环在一定条件下的织积分解以及矩形Clifford双半环是矩形双环的强分配格的充分必要条件。By using distributive lattice of bi-semirings and band bi-semiring, the concepts of rectangular bi-ring and rectangular Clifford bi-semiring are obtained by extending left bi-ring and left Clifford bi-semiring. The characterizations of rectangular bi-ring and rectangular Clifford bi-semiring are given. Under certain conditions, the spined product decomposition of rectangular Clifford bi-semiring is obtained, and the necessary and sufficient conditions for a rectangular Clifford bi-semiring to be the strong distributive lattice of rectangular bi-rings.

关 键 词：带双半环 矩形双环 矩形Clifford双半环 分配格同余 

分 类 号：O152.7[理学—数学]