Abstract
Green's rather abstract theory of G-functors is used to derive quite formally many results concerning the structure and the functorial behaviour of relative Grothendieck rings starting with a basic induction theorem. These results are developed and discussed with particular regard to the closely related results proved by I. Reiner and T. Y. Lam with module theoretic methods. The proof of the induction theorem is based on the theory of Burnside rings and multiplicative induction techniques.
Keywords
- Finite Group
- Direct Summand
- Isomorphism Class
- Ring Homomorphism
- Grothendieck Group
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Supported in part by National Science Foundation grant GP-36418X2.
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© 1975 Springer-Verlag
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Dress, A.W.M. (1975). On relative Grothendieck rings. In: Dlab, V., Gabriel, P. (eds) Representations of Algebras. Lecture Notes in Mathematics, vol 488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081218
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DOI: https://doi.org/10.1007/BFb0081218
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