Semistar linkedness and flatness, Prüfer semistar multiplication domains

Details Semistar linkedness and flatness, Prüfer semistar multiplication domains Semistar linkedness and flatness, Prüfer semistar multiplication domains

2003-05-23

arxiv.org/abs/math/0305333v1

Mathematics

Commutative Algebra

24 pages

Scientific paper

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 Pr\"ufer domains for Pr\"ufer semistar multiplication domains.

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