F-rationality of the ring of modular invariants

JOURNAL OF ALGEBRA

卷:484

Article

Hashimoto, Mitsuyasu¹ 

[1] Okayama Univ, Okayama 7008530, Japan

关键词: F-rational;    F-regular;    Dual F-signature;    Frobenius limit;   

DOI  :  10.1016/j.jalgebra.2017.04.017

来源: Elsevier

【 摘 要 】

Using the description of the Frobenius limit of modules over the ring of invariants under an action of a finite group on a polynomial ring over a field of characteristic p > 0 developed by Symonds and the author, we give a characterization of the ring of invariants with a positive dual F-signature. Combining this result and Kemper's result on depths of the ring of invariants under an action of a permutation group, we give an example of an F-rational, but non-F-regular ring of invariants under the action of a finite group. (c) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free