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- W2057646624 abstract "HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button. 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. For a commutative local ring $R$, $n=3,4$, and $m, k, s in {mathbb N}$ it is proved that ${mathbb M}_n(R)$ is strongly clean if and only if ${mathbb M}_n(R[[x]])$ is strongly clean if and only if ${mathbb M}_n(R[[x_1, x_2, ldots, x_m]])$ is strongly clean if and only if $ {mathbb M}_n(frac{R[x]}{(x^{k})})$ is strongly clean if and only if $ {mathbb M}_n(dfrac{R[x_{1}, x_{2}, ldots , x_{s}]}{(x^{n_1}_{1}, x^{n_{2}}_{2}, ldots , x^{n_{s}}_{s})}) $ is strongly clean if and only if ${mathbb M}_n(R propto R)$ is strongly clean where $ Rpropto R={scriptsize(begin{array}{@{}c@{quad}c@{}} a& b 0& a end{array}): a, b in R }$ is the trivial extension of $R$. This extends a result of J. Chen, X. Yang and Y. Zhou [$mathbf{5}$] from $n=2$ to 3 and 4." @default.
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- W2057646624 date "2006-09-01" @default.
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- W2057646624 title "ON STRONGLY CLEAN MATRIX RINGS" @default.
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- W2057646624 doi "https://doi.org/10.1017/s0017089506003284" @default.
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