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- W2394794637 abstract "Let D be an integral domain, t be the so-called t-operation on D; and S be a (not necessarily saturated) multiplicative subset of D. In this paper, we study the Nagata ring of S-Noetherian domains and locally S-Noetherian domains. We also inves- tigate the t-Nagata ring of t-locally S-Noetherian domains. In fact, we show that if S is an anti-archimedean subset of D, then D is an S-Noetherian domain (respectively, locally S-Noetherian domain) if and only if the Nagata ring D(X)N is an S-Noetherian domain (respectively, locally S-Noetherian domain). We also prove that if S is an anti-archimedean subset of D, then D is a t-locally S-Noetherian domain if and only if the polynomial ring D(X) is a t-locally S-Noetherian domain, if and only if the t-Nagata ring D(X)Nv is a t-locally S-Noetherian domain." @default.
- W2394794637 created "2016-06-24" @default.
- W2394794637 creator A5035198343 @default.
- W2394794637 date "2015-09-23" @default.
- W2394794637 modified "2023-09-29" @default.
- W2394794637 title "A Note on S-Noetherian Domains" @default.
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- W2394794637 doi "https://doi.org/10.5666/kmj.2015.55.3.507" @default.
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