DOCUMENTA MATHEMATICA, Vol. 1 (1996), 149-197

Manfred Knebusch and Digen Zhang

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.

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