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- Title
SUMS OF UNITS IN RINGS.
- Authors
GROVER, HARPREET K.; WANG, ZHOU; KHURANA, DINESH; CHEN, JIANLONG; LAM, T. Y.
- 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.
- Subjects
UNIT groups (Ring theory); RING theory; ADDITION (Mathematics); NUMBER systems; MATHEMATICAL analysis; ABSTRACT algebra; VON Neumann regular rings
- Publication
Journal of Algebra & Its Applications, 2014, Vol 13, Issue 1, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498813500722