## Some families of strongly clean rings.(English)Zbl 1122.16027

A ring $$R$$ with identity is called strongly clean if every element of $$R$$ is the sum of an idempotent and a unit that commute with each other. For a commutative local ring and for an arbitrary integer $$n\geq 2$$, this paper deals with the question whether the strongly clean property of $$\mathbb{M}_n(R[\![x]\!])$$, $$\mathbb{M}_n(R[x]/(x^k))$$, and $$\mathbb{M}_n(RC_2)$$ follows from the strongly clean property of $$\mathbb{M}_n(R)$$. This is “yes” if $$n=2$$ by a known result.

### MSC:

 16U60 Units, groups of units (associative rings and algebras) 16S50 Endomorphism rings; matrix rings 16S36 Ordinary and skew polynomial rings and semigroup rings
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### References:

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