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基于可减的实半环与实素理想
引用本文:敖忠平,陈培慈,肖烈虹.基于可减的实半环与实素理想[J].纯粹数学与应用数学,2010,26(3):353-355.
作者姓名:敖忠平  陈培慈  肖烈虹
作者单位:石油大学(广州)计算机科学系,广东,广州,510510;江西师范大学数学系,江西,南昌,330027;南方医科大学生物医学工程学院数理系,广东,广州,510515
基金项目:江西省教育厅科研基金 
摘    要:半环R被称为实半环,若对于任意的n∈N,方程x1^2+…+xn^2=0在R中只有零解:x1=…=xn=0.为了刻画实半环,引入了实理想和极小素理想的概念,利用同余的方法,得到了可减半环类中实半环的结构定理.

关 键 词:可减子集  可减半环  实半环  实素理想

Real semiring based on being subtractive and real prime ideals
AO Zhong-ping,CHEN Pei-ci,XIAO Lie-hong.Real semiring based on being subtractive and real prime ideals[J].Pure and Applied Mathematics,2010,26(3):353-355.
Authors:AO Zhong-ping  CHEN Pei-ci  XIAO Lie-hong
Institution:AO Zhong-ping 1,CHEN Pei-ci 2,XIAO Lie-hong 3(1.Department of Computer Science,University of Petroleum(Guangzhou),Guangzhou 510510,China,2.Department of Mathematics,Jiangxi Normal University,Nanchang 330027,3.Department of Mathematics and Physics,School of Biomedical Engineering of Southern Medical University,Guangzhou 510515,China)
Abstract:A semiring R is called a real semiring if an equation that x1^2+…+xn^2 = 0 only has zero solutions in R: x1 =…= xn = 0.In order to describe the real semings,the methods of congruences are used,the conceptions of real ideals and minimal prime ideals are introduced in the paper.The structure theorems of real semirings in the class of the subtractive semirings are obtained.
Keywords:subtractive subset  subtractive semiring  real semiring  real prime ideals  
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