Manfred Knebusch and Digen Zhang

摘要

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 muchthe same way as Prüfer domains to Krull valuations. We develop abasic theory of Prüfer extensions and give some examples. In theintroduction we try to explain why Prüfer extensions deserveinterest from a geometric viewpoint.