Fine rings: A new class of simple rings

被引：33

作者：

Calugareanu, G. ^{[1
]}

Lam, T. Y. ^{[2
]}

机构：

[1] Univ Babes Bolyai, Dept Math & Comp Sci, Kogalniceanu St, Cluj Napoca 400084, Romania

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2016年 / 15卷 / 09期

关键词：

Units; nilpotents; matrix rings; artinian rings; simple rings; clean rings; fine rings; UU rings; ELEMENTS;

D O I：

10.1142/S0219498816501735

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A nonzero ring is said to be fine if every nonzero element in it is a sum of a unit and a nilpotent element. We show that fine rings form a proper class of simple rings, and they include properly the class of all simple artinian rings. One of the main results in this paper is that matrix rings over fine rings are always fine rings. This implies, in particular, that any nonzero (square) matrix over a division ring is the sum of an invertible matrix and a nilpotent matrix.

引用

页数：18

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