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A Note on S-Noetherian Domains
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  • Journal title : Kyungpook mathematical journal
  • Volume 55, Issue 3,  2015, pp.507-514
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2015.55.3.507
 Title & Authors
A Note on S-Noetherian Domains
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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 investigate 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 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 is a t-locally S-Noetherian domain.
S-Noetherian domain;(t-)locally S-Noetherian domain;(t-)Nagata ring;finite (t-)character;
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