A nil-clean 2 × 2 matrix over the integers which is not clean-Reference-Cited by-同舟云学术

A nil-clean 2 × 2 matrix over the integers which is not clean

Published:2014-04-20 Issue:06 Volume:13 Page:1450009
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Andrica Dorin¹,Călugăreanu Grigore¹

Affiliation:

1. Department of Mathematics and Computer Science, Babes-Bolyai University, 1 Kogalniceanu Street, 400084 Cluj-Napoca, Romania

Abstract

While any nil-clean ring is clean, the last eight years, it was not known whether nil-clean elements in a ring are clean. We give an example of nil-clean element in the matrix ring ℳ2(Z) which is not clean.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498814500091

Reference5 articles.

1. An Introduction to Diophantine Equations

2. A CHARACTERIZATION OF UNIT REGULAR RINGS

3. Nil clean rings

4. Clean matrices and unit-regular matrices

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