Fine环的一类推广
A kind of generalization of fine rings
崔雨茹 1程杨1
作者信息
- 1. 安徽师范大学数学与统计学院,安徽芜湖 241000
- 折叠
摘要
称R是fine环,如果R中任意非零元素均可表示为一个可逆元与一个幂零元之和.作为fine环的一类推广,本文引入J#-fine环的概念,研究了J#-fine环的基本性质及其与相关环类的关系,讨论了矩阵扩张的J#-fine性质,证明了 J*-fine环上的任意矩阵环均是J#-fine的.
Abstract
A ring R is fine if every nonzero element of R is the sum of a unit and a nilpotent.We introduce the concept of J#-fine rings as a generalization of fine rings,and study basic properties of J*-fine rings and the relationship between J*-fine rings and rings which associate with J#-fine rings.We discuss the J#-fineness of matrix expansion and prove that any matrix rings over J*-fine rings are J#-fine.
关键词
fine环/J#-fine环/矩阵环Key words
fine ring/J#-fine ring/matrix ring引用本文复制引用
基金项目
安徽省高校自然科学重点基金项目(2008085MA06)
安徽省高校优秀青年人才计划项目(gxyqZD2019009)
出版年
2024
NETL
NSTL
万方数据