Prüfer $\star$--multiplication domains and semistar operations
| dc.creator | Fontana, Marco | |
| dc.creator | Jara, Pascual | |
| dc.creator | Santos, Eva | |
| dc.date | 2002-11-26 | |
| dc.date.accessioned | 2026-07-07T04:53:19Z | |
| dc.date.available | 2026-07-07T04:53:19Z | |
| dc.description | We prove a characterization of a P$\star$MD, when $\star$ is a semistar operation, in terms of polynomials (by using the classical characterization of Prüfer domains, in terms of polynomials given by R. Gilmer and J. Hoffman \cite{Gilmer/Hoffmann:1974}, as a model), extending a result proved in the star case by E. Houston, S.J. Malik and J. Mott \cite{Houston/Malik/Mott:1984}. We also deal with the preservation of the P$\star$MD property by ``ascent'' and ``descent'' in case of field extensions. In this context, we generalize to the P$\star$MD case some classical results concerning Prüfer domains and P$v$MDs. In particular, we reobtain as a particular case a result due to H. Prüfer \cite{Prufer} and W. Krull \cite{Krull:1936} (cf. also F. Lucius \cite{Lucius:1998} and F. Halter-Koch \cite{Koch:2000}). Finally, we develop several examples and applications when $\star$ is a (semi)star given explicitly (e.g. we consider the case of the ``standard'' $v$--, $t$--, $b$--, $w$--operations or the case of semistar operations associated to appropriate families of overrings). | |
| dc.identifier | https://arxiv.org/abs/math/0211410 | |
| dc.identifier | http://arxiv.org/abs/math/0211410 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65797 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13F05; 13A15; 13A18; 13F30 | |
| dc.title | Prüfer $\star$--multiplication domains and semistar operations | |
| dc.type | text |