Grothendieck groups of abelian group rings |
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Authors: | HW Lenstra |
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Institution: | Mathematisch Instituut, Universiteit van Amsterdam, The Netherlands |
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Abstract: | Let R be a noetherian ring, and G(R) the Grothendieck group of finitely generated modules over R. For a finite abelian group π, we describe G(Rπ) as the direct sum of groups G(R'). Each R' is the form Rζn, 1/n], where n is a positive integer and ζn a primitive nth root of unity. As an application, we describe the structure of the Grothendiek group of pairs (H, u), where H is an abelian group and u is an automorphism of H of finite order. |
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