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Abstract
In 1994, Matsuda and Okabe introduced the notion of semistar operation, extending the “classical” concept of star operation. In this paper, we introduce and study the notions of semistar linkedness and semistar flatness which are natural generalizations, to the semistar setting, of their corresponding “classical” concepts. As an application, among other results, we obtain a semistar version of Davis' and Richman's overring-theoretical theorems of characterization of Prüfer domains for Prüfer semistar multiplication domains.
Acknowledgments
Both authors are grateful to F. Halter-Koch for providing them with a copy of his recent pre-print Characterization of Prüfer multiplication monoids and domains by means of spectral module theory, presented at the Algebra Conference (Venezia, June 2002). Using the language of monoids and module systems, Halter-Koch's work sheds further light on some of the themes discussed in the present paper.
During the preparation of this work, the second named author was supported in part by research grants MIUR 2001/2002 (Cofin 2000-MM01192794) and 2003/04 (Cofin 2002-2002013989).
Notes
#Communicated by R. Villarreal.