Strong cleanness of the 2× 2 matrix ring over a general local ring

2008/05/03 by Xiande Yang, Yang, Xiande, Yiqiang Zhou +1
Mathematics · #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.0805.0359

openalex publication_date 2008/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A ring R is called strongly clean if every element of R is the sum of a unit and an idempotent that commute with each other. A recent result of Borooah, Diesl and Dorsey \citeBDD05a completely characterized the commutative local rings R for which \mathbb M_n(R) is strongly clean. For a general local ring R and n>1, however, it is unknown when the matrix ring \mathbb M_n(R) is strongly clean. Here we completely determine the local rings R for which \mathbb M₂(R) is strongly clean.

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