G-prime and G-primary G-ideals on G-schemes
نویسندگان
چکیده
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.
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