### Abstract

It is known that a certain invariant subring R has finite F-representation type. Thus, we can write the R-module Re as a finite direct sum of finitely many R-modules. In such a decomposition of Re, we pay attention to the multiplicity of each direct summand. For the multiplicity of free direct summand, there is the notion of F-signature defined by C. Huneke and G. Leuschke and it characterizes some singularities. In this paper, we extend this notion to non-free direct summands and determine their explicit values.

Original language | English |
---|---|

Pages (from-to) | 142-152 |

Number of pages | 11 |

Journal | Journal of Algebra |

Volume | 443 |

DOIs | |

Publication status | Published - Dec 1 2015 |

### Fingerprint

### Keywords

- F-signature
- Finite f-representation type
- Invariant subrings

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Algebra*,

*443*, 142-152. https://doi.org/10.1016/j.jalgebra.2015.06.039

**Generalized F-signature of invariant subrings.** / Hashimoto, Mitsuyasu; Nakajima, Yusuke.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 443, pp. 142-152. https://doi.org/10.1016/j.jalgebra.2015.06.039

}

TY - JOUR

T1 - Generalized F-signature of invariant subrings

AU - Hashimoto, Mitsuyasu

AU - Nakajima, Yusuke

PY - 2015/12/1

Y1 - 2015/12/1

N2 - It is known that a certain invariant subring R has finite F-representation type. Thus, we can write the R-module Re as a finite direct sum of finitely many R-modules. In such a decomposition of Re, we pay attention to the multiplicity of each direct summand. For the multiplicity of free direct summand, there is the notion of F-signature defined by C. Huneke and G. Leuschke and it characterizes some singularities. In this paper, we extend this notion to non-free direct summands and determine their explicit values.

AB - It is known that a certain invariant subring R has finite F-representation type. Thus, we can write the R-module Re as a finite direct sum of finitely many R-modules. In such a decomposition of Re, we pay attention to the multiplicity of each direct summand. For the multiplicity of free direct summand, there is the notion of F-signature defined by C. Huneke and G. Leuschke and it characterizes some singularities. In this paper, we extend this notion to non-free direct summands and determine their explicit values.

KW - F-signature

KW - Finite f-representation type

KW - Invariant subrings

UR - http://www.scopus.com/inward/record.url?scp=84938833645&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84938833645&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2015.06.039

DO - 10.1016/j.jalgebra.2015.06.039

M3 - Article

AN - SCOPUS:84938833645

VL - 443

SP - 142

EP - 152

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -