Prüfer ⋆--multiplication domains and ⋆--coherence

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The purpose of this paper is to deepen the study of the Prüfer ⋆--multiplication domains, where ⋆ is a semistar operation. For this reason, in Section 2, we introduce the ⋆--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 ⋆--multiplication domains. In particular, in Section 3, we obtain a characterization of Prüfer ⋆--multiplication domains in terms of ⋆--domains satisfying a variety of coherent-like conditions. In Section 4, we extend to the semistar setting the notion of H--domain introduced by Glaz and Vasconcelos and we show, among the other results that, in the class of the H(⋆)--domains, the Prüfer ⋆--multiplication domains coincide with the ⋆--domains.