English

Idealisers in Skew Group Rings

Rings and Algebras 2020-09-24 v1

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.

Keywords

Cite

@article{arxiv.1811.10366,
  title  = {Idealisers in Skew Group Rings},
  author = {Ruth A. Reynolds},
  journal= {arXiv preprint arXiv:1811.10366},
  year   = {2020}
}

Comments

17 pages; comments welcome

R2 v1 2026-06-23T05:27:59.534Z