$G$-prime and $G$-primary $G$-ideals on $G$-schemes

Mitsuyasu Hashimoto; Mitsuhiro Miyazaki

doi:10.1080/00927872.2012.656335

$G$-prime and $G$-primary $G$-ideals on $G$-schemes

Commutative Algebra 2014-09-30 v4 Algebraic Geometry

Authors: Mitsuyasu Hashimoto , Mitsuhiro Miyazaki

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Abstract

Let $G$ be a flat finite-type group scheme over a scheme $S$ , and $X$ a noetherian $S$ -scheme on which $G$ -acts. We define and study $G$ -prime and $G$ -primary $G$ -ideals on $X$ and study their basic properties. In particular, we prove the existence of minimal $G$ -primary decomposition and the well-definedness of $G$ -associated $G$ -primes. We also prove a generalization of Matijevic-Roberts type theorem. In particular, we prove Matijevic-Roberts type theorem on graded rings for $F$ -regular and $F$ -rational properties.

Keywords

ideal theory finite group theory monomial ideals

Cite

@article{arxiv.0906.1441,
  title  = {$G$-prime and $G$-primary $G$-ideals on $G$-schemes},
  author = {Mitsuyasu Hashimoto and Mitsuhiro Miyazaki},
  journal= {arXiv preprint arXiv:0906.1441},
  year   = {2014}
}

Comments

54pages, added Example 6.16 and the reference [8]. The final version

$G$-prime and $G$-primary $G$-ideals on $G$-schemes

Abstract

Keywords

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