Geodesic
About $k$-nil-good formal matrix rings
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 77 (2022), pp. 17-26

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In 2018, Abdolyusefi, Ashrafi, and Chen gave a definition of a $2$-nil-good ring element in their work, generalizing the notion of a graceful ring element introduced two years earlier by Kalugeryan and Lam, as well as the definition of a $2$-nil-good ring. In the same work, it was shown that the Morita context ring, i.e. a formal matrix ring of the second order is $2$-nil-good if the rings over which it is considered are themselves $2$-nil-good. In this paper, we generalize further, defining $k$-nil-good elements and $k$-nil-good rings, and state a condition under which a formal matrix ring of an arbitrary finite order is $k$-nil-good.
Keywords: ring, $k$-nil-good ring, formal matrix ring
Mots-clés : Morita context. 
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     author = {Ts. D. Norbosambuev and E. A. Timoshenko},
     title = {About $k$-nil-good formal matrix rings},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {17--26},
     publisher = {mathdoc},
     number = {77},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2022_77_a1/}
}
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Ts. D. Norbosambuev; E. A. Timoshenko. About $k$-nil-good formal matrix rings. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 77 (2022), pp. 17-26. http://geodesic.mathdoc.fr/item/VTGU_2022_77_a1/