半环上的幂零理想(英文)  

Nilpotent Ideals over Hemirings

作　　者：丰建文[1] 黄福生[1] 

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330027

出　　处：《江西师范大学学报（自然科学版）》2005年第4期305-308,共4页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：江西省自然科学基金资助项目(0211022).

摘　　要：该文研究了半环上的幂零与幂零元理想,得出在阿丁半环上的关于幂零理想与幂零元理想的定义是等价的,且还引进了完全可减半环,并证明出任一个阿丁(诺特)完全可减半环R必存在一个极大幂零理想B,满足:B包含所有幂零单边理想,并且商半环R/B没有非零幂零理想.In this paper the notion of subtractive ideal and completely subtractive hemiring are introduced. In the third section it is proved that the definition of nil ideal over an artin herniring is in fact equivalent to the definition of nilpotent ideal. Moreover, we show that an artin （noether） herniring R which is completely subtractive has a unique maximal nilpotent ideal B satisfying that B contains all nilpotent one-sided ideals of R and the factor hemiring R/B doesn＇t have nilpotent ideals.

关 键 词：半环 幂零理想 幂零元理想 完全可减半环 

分 类 号：O153.3[理学—数学]