SUMS OF UNITS IN RINGS

被引：9

作者：

Grover, Harpreet K. ^{[1
]}

Wang, Zhou ^{[2
]}

Khurana, Dinesh ^{[3
]}

Chen, Jianlong ^{[2
]}

Lam, T. Y. ^{[4
]}

机构：

[1] Guru Nanak Dev Univ, Dept Math, Amritsar 143005, Punjab, India

[2] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China

[3] Panjab Univ, Dept Math, Chandigarh 160014, India

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

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2014年 / 13卷 / 01期

关键词：

Sums of units; n-sum property; unit sum number; unit-regular rings; exchange rings; strongly pi-regular rings; STABLE RANGE; CANCELLATION; NUMBERS;

D O I：

10.1142/S0219498813500722

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study rings that are additively generated by units. We prove that if the identity in a ring with stable range one is a sum of two units, then every (von Neumann) regular element is a sum of two units. It follows that every element in a unit-regular ring is a sum of two units if the identity is a sum of two units. Also, if the identity of a strongly pi-regular ring is a sum of two units, then every element is a sum of three units.

引用

页数：10

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