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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.… Click to show full abstract
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 ◁ 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:
skew group;
group rings;
ideal;
idealisers skew;
group
Journal Title: Journal of Algebra
Year Published: 2019
Link to full text (if available)
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Journal Title: Journal of Algebra
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!