Reductive derivations of local rings of characteristic p
Let A be a commutative noetherian algebra over the field with p elements. A notion of reductive derivations \(d: A\to A\) is introduced in terms of rings of differential operators. In particular, the semisimple derivations are reductive. It is shown that for an arbitrary derivation of a local ring, the study of its constants may be reduced to the case when the derivation maps the ring into its maximal ideal. Moreover, if the original derivation is reductive, the modified one is semisimple. It is proved that the rings of constants of reductive derivations inherit the Buchsbaum and the Cohen-Macaulay properties. The Gorenstein descent is investigated. A Hinič character of a semisimple derivation is defined and the canonical module of the ring of constants is described in terms of it.
canonical module of the ring of constants
scientific article; zbMATH DE number 4012772
scientific article