Abstract
The Nagata ring R(X) and the Serre’s conjecture ring R⟨X⟩ are two localizations of the polynomial ring R[X] at the polynomials of unit content and at the monic polynomials, respectively. In this paper, we contribute to the study of Prüfer conditions in R(X) and R⟨X⟩. In particular, we solve the four open questions posed by Glaz and Schwarz in Section 8 of their survey paper [38] related to the transfer of Prüfer conditions to these two constructions.
| Original language | English |
|---|---|
| Pages (from-to) | 2073-2082 |
| Number of pages | 10 |
| Journal | Communications in Algebra |
| Volume | 46 |
| Issue number | 5 |
| DOIs | |
| State | Published - 4 May 2018 |
Bibliographical note
Publisher Copyright:© 2017 Taylor & Francis.
Keywords
- Arithmetical ring
- Gaussian ring
- Nagata ring
- Prüfer domain
- Prüfer ring
- Serre’s conjecture ring
- fqp-ring
- semihereditary ring
- weak dimension
ASJC Scopus subject areas
- Algebra and Number Theory