Abstract
A great deal of work has been done in the last ten years on actions of finite groups on non-commutative rings. However, many questions remain open, and we shall discuss here fifteen such questions. These problems are all related to a common circle of ideas which have roots in the classical theory of commutative algebra and invariant theory. In particular, our topics include integrality, prime ideals, chain conditions, and invariants of generic matrix rings. For each question, we survey the known parital results; additionally, in the section on prime ideals, we give some new proofs and even some new results. Finally, we discuss the problem of classifying the actions of a given group on a specific ring.
Work partially supported by NSF Grant MCS 83-01393. The author also wishes to thank F. Van Oystaeyen for organizing this conference.
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Montgomery, S. (1984). Group Actions on Rings: Some Classical Problems. In: van Oystaeyen, F. (eds) Methods in Ring Theory. NATO ASI Series, vol 129. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6369-6_24
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