### Abstract

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.

Original language | English |
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Pages (from-to) | 207-223 |

Number of pages | 17 |

Journal | Journal of Algebra |

Volume | 484 |

DOIs | |

Publication status | Published - Aug 15 2017 |

### Fingerprint

### Keywords

- Dual F-signature
- F-rational
- F-regular
- Frobenius limit

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Algebra*,

*484*, 207-223. https://doi.org/10.1016/j.jalgebra.2017.04.017

**F-rationality of the ring of modular invariants.** / Hashimoto, Mitsuyasu.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 484, pp. 207-223. https://doi.org/10.1016/j.jalgebra.2017.04.017

}

TY - JOUR

T1 - F-rationality of the ring of modular invariants

AU - Hashimoto, Mitsuyasu

PY - 2017/8/15

Y1 - 2017/8/15

N2 - 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.

AB - 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.

KW - Dual F-signature

KW - F-rational

KW - F-regular

KW - Frobenius limit

UR - http://www.scopus.com/inward/record.url?scp=85019086903&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019086903&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2017.04.017

DO - 10.1016/j.jalgebra.2017.04.017

M3 - Article

AN - SCOPUS:85019086903

VL - 484

SP - 207

EP - 223

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -