Vol. 36, No. 2, 1971

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Divisor classes in pseudo Galois extensions

William Charles Waterhouse

Vol. 36 (1971), No. 2, 541–548

Let R be a Krull domain with fraction field K. Let L be a finite extension of K, and let S be the integral closure of R in L; then S is also a Krull domain. Let 𝒫(R,S) be the group of divisor classes in R becoming principal in S. Suppose there is a group scheme (or Hopf algebra) acting on S with fixed ring R. Then there is a cohomology group which contains 𝒫(R,S) and equals it if the action is Galois at each minimal prime. This generalizes and unifies some results of Samuel.

Mathematical Subject Classification
Primary: 13.70
Received: 16 December 1969
Published: 1 February 1971
William Charles Waterhouse