## 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 $$n$$.

### MSC:

 16S50 Endomorphism rings; matrix rings 16U60 Units, groups of units (associative rings and algebras)
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### References:

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