On strongly clean matrix and triangular matrix rings. (English) Zbl 1114.16024

A ring \(R\) is called strongly clean if every element of \(R\) is the sum of an idempotent and a unit that commute. In this paper the authors obtain new families of strongly clean rings through matrix rings and triangular matrix rings. For instance, it is proved that the \(2\times 2\) matrix ring over the ring of \(p\)-adic integers and the triangular matrix ring over a commutative semiperfect ring are all strongly clean. For a commutative ring \(R\), the authors prove that the \(n\times n\) upper triangular matrix ring over \(R\) is strongly clean for every \(n\).


16S50 Endomorphism rings; matrix rings
16U60 Units, groups of units (associative rings and algebras)
Full Text: DOI


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