Let k be an integer greater than or equal to 2. The ring R is said to be k-good if every element of R is the sum of k invertible elements of R. We have showed that the ring of formal row-finite matrices will be k-good if all rings from its main diagonal are k-good. Some applications of this result are given, in particular, to the problem of k-goodness of the ring of endomorphisms of decomposable module or Abelian group.

中文翻译：

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k-Good 无穷阶形式矩阵环

让ķ是一个整数大于或等于2的环- [R被认为是ķ -good如果每个元素- [R是的总和ķ的可逆元件ř。我们已经证明，如果所有来自其主对角线的环都是k - good，那么正式的行有限矩阵环将是k - good。给出了这个结果的一些应用，特别是可分解模或阿贝尔群的自同态环的k优度问题。