Geodesic
$k$-good formal matrix rings of infinite order
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2021), pp. 35-42

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Let $k$ be an integer that is 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. Also some applications of this result are given, particularly to the problem of $k$-goodness of the ring of endomorphisms of decomposable module or Abelian group.
Keywords: $k$-good element, $k$-good ring, ring of formal matrices of infinite order. 
@article{IVM_2021_6_a3,
     author = {P. A. Krylov and Ts. D. Norbosambuev},
     title = {$k$-good formal matrix rings of infinite order},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {35--42},
     publisher = {mathdoc},
     number = {6},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_6_a3/}
}
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P. A. Krylov; Ts. D. Norbosambuev. $k$-good formal matrix rings of infinite order. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2021), pp. 35-42. http://geodesic.mathdoc.fr/item/IVM_2021_6_a3/