Prüfer $\star$--multiplication domains and $\star$--coherence

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dc.creatorFontana, Marco
dc.creatorPicozza, Giampaolo
dc.date2006-06-27
dc.date.accessioned2026-07-07T07:17:43Z
dc.date.available2026-07-07T07:17:43Z
dc.descriptionThe purpose of this paper is to deepen the study of the Prüfer $\star$--multiplication domains, where $\star$ is a semistar operation. For this reason, in Section 2, we introduce the $\star$--domains, as a natural extension of the $v$--domains, where $v$ is the classical Artin's divisorial operation. We investigate their close relation with the Prüfer $\star$--multiplication domains. In particular, in Section 3, we obtain a characterization of Prüfer $\star$--multiplication domains in terms of $\star$--domains satisfying a variety of coherent-like conditions. In Section 4, 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 $\star$--multiplication domains coincide with the $\star$--domains.
dc.identifierhttps://arxiv.org/abs/math/0606671
dc.identifierhttp://arxiv.org/abs/math/0606671
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/114041
dc.subjectCommutative Algebra
dc.subject13F05; 13G05; 13E99
dc.titlePrüfer $\star$--multiplication domains and $\star$--coherence
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