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- W3208927265 abstract "Let $mathfrak{R}$ be an associative ring graded by left cancellative monoid$mathsf{S}$, and $e$ the neutral element of $mathsf{S}$. We study thefollowing problem: if $mathfrak{R}_e$ is nil, then is $mathfrak{R}$nil/nilpotent? We have proved that if $mathfrak{R}_e$ is nil (of boundedindex) and $mathsf{f}$- commutative, then $mathfrak{R}$ is nil (of boundedindex). Later, we have shown that $mathfrak{R}_e$ being nilpotent implies$mathfrak{R}$ is nilpotent. Consequently, we have exhibited a generalizationof Dubnov-Ivanov-Nagata-Higman Theorem for the graded algebras case.Furthermore, we have exhibited relations between graded rings and the problemsof K{o}the and Kurosh-Levitzki. We have proved that graded rings and$mathsf{f}$-commutative rings provide positive solutions to these problems." @default.
- W3208927265 created "2021-11-08" @default.
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- W3208927265 date "2021-10-23" @default.
- W3208927265 modified "2023-09-27" @default.
- W3208927265 title "K{o}the's Problem, Kurosch-Levitzki Problem and Graded Rings]{K{o}the's Problem, Kurosch-Levitzki Problem and Graded Rings" @default.
- W3208927265 hasPublicationYear "2021" @default.
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