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Does there exist a book discussing algorithmic invariant theory for finite groups that does not assume that the algebras involved are defined over a field (e.g. base rings $\mathbb{Z}$ and $\mathbb{Z}/n$ are allowed)? I could not find one though I can not claim a good knowledge of the literature.

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  • $\begingroup$ a related thread mathoverflow.net/questions/279253/invariant-theory-over-rings $\endgroup$ – user143954 Aug 4 at 13:35
  • $\begingroup$ especially Gregor Kemper's comment- For finite groups, algorithms for computing the invariant ring over a base ring such as the integers are given in G. Kemper, Using Extended Derksen Ideals in Computational Invariant Theory, J. Symbolic Comput. 72 (2016), 161-181. $\endgroup$ – user143954 Aug 4 at 13:36

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