### 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 |
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Pages (from-to) | 142-152 |

Number of pages | 11 |

Journal | Journal of Algebra |

Volume | 443 |

DOIs | |

Publication status | Published - Dec 1 2015 |

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Hashimoto, M., & Nakajima, Y. (2015). Generalized F-signature of invariant subrings.

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