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Prüfer ⋆–multiplication domains and ⋆–coherence
| Content Provider | Semantic Scholar |
|---|---|
| Author | Fontana, Marco Picozza, Giampaolo |
| Copyright Year | 2006 |
| Abstract | The purpose of this paper is to deepen the study of the Prüfer ⋆–mul-tiplication domains, where ⋆ is a semistar operation. For this reason, we introduce the ⋆–domains, as a natural extension of the v-domains. We investigate their close relation with the Prüfer ⋆-multiplication domains. In particular, we obtain a characterization of Prüfer ⋆-multiplication domains in terms of ⋆–domains satisfying a variety of coherent-like conditions. We extend to the semistar setting the notion of $\texttt{H}$-domain introduced by Glaz and Vasconcelos and we show, among the other results that, in the class of the $\texttt{H}(\star)$–domains, the Prüfer ⋆-multiplication domains coincide with the ⋆-domains. Keywords: Star and semistar operation, Prüfer (⋆-multiplication) domain, $\texttt{H}$-domain, Localizing system, Coherent domain, Divisorial and invertible idealMathematics Subject Classification (2000): 13F05, 13G05, 13E99 |
| Starting Page | 145 |
| Ending Page | 170 |
| Page Count | 26 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s11587-006-0010-1 |
| Volume Number | 55 |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0606671v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
