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Proceedings of the American Mathematical Society

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Finite generation of class groups of rings of invariants

Author: Andy R. Magid
Journal: Proc. Amer. Math. Soc. 60 (1976), 45-48
MSC: Primary 13D15; Secondary 20G30
MathSciNet review: 0427306
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Abstract: Let R be a normal affine domain over the algebraically closed field k, and let G be a connected algebraic group acting rationally on R. It is shown that the divisor class group of $ {R^G}$ is a homomorphic image of an extension of a subgroup of the class group of R by a subquotient of the character group of G. In particular, if R has finitely generated class group, so does $ {R^G}$.

References [Enhancements On Off] (What's this?)

  • [1] H. Bass, Introduction to some methods of algebraic K-theory, CBMS Regional Conf. Ser. in Math. no. 20, Amer. Math. Soc., Providence, R. I., 1974. MR 50 #441. MR 0347942 (50:441)
  • [2] M. Rosenlicht, Toroidal algebraic groups, Proc. Amer. Math. Soc. 12 (1961), 984-988. MR 24 #A3162. MR 0133328 (24:A3162)

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Article copyright: © Copyright 1976 American Mathematical Society

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