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- W4320735144 abstract "In this paper, we present a noncommutative scheme theory for the semi-graded rings generated in degree one defined by Lezama and Latorre cite{LezamaLatorre2017} following the ideas about schematicness introduced by Van Oystaeyen and Willaert cite{VanOystaeyenWillaert1995} for $mathbb{N}$-graded algebras. With this theory, we prove the Serre-Artin-Zhang-Verevkin theorem cite{ArtinZhang1994, EGAII1961, Hartshorne1977, Serre1955, Verevkin1992a, Verevkin1992} for several families of non-$mathbb{N}$-graded algebras and finitely non-$mathbb{N}$-graded algebras appearing in ring theory and noncommutative algebraic geometry. Our treatment contributes to the research on this theorem presented by Lezama cite{Lezama2021, LezamaLatorre2017} from a different point of view." @default.
- W4320735144 created "2023-02-15" @default.
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- W4320735144 date "2023-01-18" @default.
- W4320735144 modified "2023-09-29" @default.
- W4320735144 title "Noncommutative scheme theory and the Serre-Artin-Zhang-Verevkin theorem for semi-graded rings" @default.
- W4320735144 doi "https://doi.org/10.48550/arxiv.2301.07815" @default.
- W4320735144 hasPublicationYear "2023" @default.
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