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http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/11471| Title: | Comment on “Two notes on imbedded prime divisors |
| Authors: | Kumar, Rahul |
| Keywords: | Mathematics Noetherian rings Normal pair Adjacent rings |
| Issue Date: | 2020 |
| Publisher: | ARXIV |
| Abstract: | The following result was proved in [5,Remark 2.2]. Theorem 0.1. If R T are Noetherian rings such that there does not exist any integrally dependent adjacent Noetherian rings between them, then for each ¯c/¯b 2 T/Z (where Z = Rad(T) = Rad(R) and ¯b, ¯c regular in R/Z), we have either ¯c/¯b 2 R/Z or ¯ b/¯c 2 R/Z, and so (R/Z)[¯c/¯b] is a localization of R/Z. |
| URI: | https://arxiv.org/pdf/2005.07214 http://dspace.bits-pilani.ac.in:8080/xmlui/handle/123456789/11471 |
| Appears in Collections: | Department of Mathematics |
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