上三角矩阵半环U_(2)(R,M)  

Upper Triangular Matrix Semiring U_(2)(R,M)

作　　者：张理江 石定琴[1] ZHANG Lijiang;SHI Dingqin(College of Science,Jiujiang University,Jiujiang,Jiangxi Province,332005 China)

机构地区：[1]九江学院理学院,江西九江332005

出　　处：《科技资讯》2021年第20期193-195,共3页Science & Technology Information

摘　　要：该文在给定的半模M上定义了上三角矩阵半环U_(2)(R,M),并利用环论的方法研究了它的相关性质,得到半环U_(2)(R,M)是加法幂等的充分必要条件是模R是加法幂等的,半环U_(2)(R,M)是零和自由的充分必要条件是半环R和半模模M都是零和自由的,以及其子半环的特征。在同构意义下,得到任何半环R都可以自然嵌入到半环U_(2)(R,M)中。In this paper,the author defines the semiring U_(2)(R,M)on the basis of the semi-module M,and studies its related properties on the method of ring theory,gets the necessary and sufficient condition that semiring U_(2)(R,M)is additive idempotent is that the semiring R is additive idempotent,and necessary and sufficient conditions for a semiring U_(2)(R,M)to be additive idempotent,zero sum free,and the characteristics of its sub semirings are obtained.In the sense of isomorphism,it is obtained that any semiring R can be naturally embedded in semirings U_(2)(R,M).

关 键 词：半环 半模 子半环 同构 

分 类 号：O153.3[理学—数学]