Manis Valuations and Prüfer Extensions I

We call a commutative ring extension $A \subset R$ Prüfer, if $A$ is an $R$-Prüfer ring in the sense of Griffin (Can.~J.~Math.~26 (1974)). These extensions relate to Manis valuations in much the same way as Prüfer domains to Krull valuations. We develop a basic theory of Prüfer extensions and give some examples. In the introduction we try to explain why Prüfer extensions deserve interest from a geometric viewpoint.

1991 Mathematics Subject Classification: Primary 13A18; Secondary 13B02, 13B30.

Full text: dvi.gz 91 k, dvi 236 k, ps.gz 174 k, pdf 434k

Home Page of DOCUMENTA MATHEMATICA