Abstract
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.
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ACKNOWLEDGMENTS
The authors are thankful to reviewer for reading the manuscript and for fruitful remarks which contributed in enhancement of the article and correction of inaccuracies in the proof of Theorem 2.
Funding
The work of the second author is funded by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-02-2020-1479/1).
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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 6, pp. 35–42.
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Krylov, P.A. k-Good Formal Matrix Rings of Infinite Order. Russ Math. 65, 29–35 (2021). https://doi.org/10.3103/S1066369X21060049
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DOI: https://doi.org/10.3103/S1066369X21060049