SUMS OF UNITS IN RINGS-Reference-Cited by-同舟云学术

SUMS OF UNITS IN RINGS

Published:2013-08-20 Issue:01 Volume:13 Page:1350072
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

GROVER HARPREET K.¹,WANG ZHOU²,KHURANA DINESH³,CHEN JIANLONG²,LAM T. Y.⁴

Affiliation:

1. Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, India

2. Department of Mathematics, Southeast University, Nanjing 210096, P. R. China

3. Department of Mathematics, Panjab University, Chandigarh 160014, India

4. Department of Mathematics, University of California, Berkeley, CA 94720, USA

Abstract

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 π-regular ring is a sum of two units, then every element is a sum of three units.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498813500722

Reference30 articles.

1. Strongly 𝜋-regular rings have stable range one

2. Diagonalization of matrices over regular rings

3. On the unit sum number of some rings

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