Manfred Knebusch and Digen Zhang
Manis valuations and Pr\"ufer extensions I
Abstract
We call a commutative ring extension $A \subset R$ Pr\"ufer, if $A$ is an $R$-Pr\"ufer ring in the sense of Griffin (Can. J. Math. 26 (1974)). These extensions relate to Manis valuations in much the same way as Pr\"ufer domains to Krull valuations. We develop a basic theory of Pr\"ufer extensions and give some examples. In the introduction we try to explain why Pr\"ufer extensions deserve interest from a geometric viewpoint.
1991 Mathematics Subject Classification: Primary 13A18; Secondary 13B02, 13B30.