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

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.

Key Words:

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

2000 Mathematics Subject Classification:

• Primary 14L30

Notes

Communicated by S. Goto.