UN-rings-Reference-Cited by-同舟云学术

UN-rings

Published:2016-11-24 Issue:10 Volume:15 Page:1650182
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Călugăreanu Grigore¹

Affiliation:

1. Department of Mathematics, Babeş-Bolyai University, 1 Kogălniceanu Street, 400084 Cluj-Napoca, Romania

Abstract

A nonzero ring is called a UN-ring if every nonunit is a product of a unit and a nilpotent element. We show that all simple Artinian rings are UN-rings and that the UN-rings whose identity is a sum of two units (e.g. if 2 is a unit), form a proper class of 2-good rings (in the sense of P. Vámos). Thus, any noninvertible matrix over a division ring is the product of an invertible matrix and a nilpotent matrix.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498816501826

Reference7 articles.

1. Two classes of rings generated by their units

2. Elementary divisors and modules

3. A First Course in Noncommutative Rings

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