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arXiv · 1811.10366

Idealisers in Skew Group Rings

Ruth A. Reynolds
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Abstract

Let C be a commutative noetherian domain, G be a finitely generated abelian group which acts on C and B = C#G be the skew group ring. For a prime ideal I in C, we study the largest subring of B in which the right ideal IB becomes a two-sided ideal - the idealiser subring. We obtain necessary and sufficient conditions for when this idealiser subring is left and right noetherian. We also give an example of these conditions in practice which translates to an interesting number theoretic problem.

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Ruth A. Reynolds. 2018-11-26. Idealisers in Skew Group Rings. https://doi.org/10.1016/j.jalgebra.2019.06.045

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