G-Prime and G-Primary G-Ideals on G-Schemes

Mitsuyasu Hashimoto, Mitsuhiro Miyazaki

Research output: Contribution to journalArticle

2 Citations (Scopus)

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-prime G-ideals. 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.

Original languageEnglish
Pages (from-to)2254-2296
Number of pages43
JournalCommunications in Algebra
Volume41
Issue number6
DOIs
Publication statusPublished - May 2013
Externally publishedYes

Fingerprint

Primary Decomposition
Graded Ring
Group Scheme
Noetherian
Finite Type
Theorem
Generalization

Keywords

  • G-associated G-prime G-ideal
  • G-primary G-ideal
  • G-prime G-ideal
  • Matijevic-Roberts type theorem

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

G-Prime and G-Primary G-Ideals on G-Schemes. / Hashimoto, Mitsuyasu; Miyazaki, Mitsuhiro.

In: Communications in Algebra, Vol. 41, No. 6, 05.2013, p. 2254-2296.

Research output: Contribution to journalArticle

Hashimoto, Mitsuyasu ; Miyazaki, Mitsuhiro. / G-Prime and G-Primary G-Ideals on G-Schemes. In: Communications in Algebra. 2013 ; Vol. 41, No. 6. pp. 2254-2296.
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