Pseudo-derivations and modular invariant theory (Q1742063)

Let \(k\) be a field of prime characteristic \(p\). In the paper under review the author introduces the notion of a pseudo-derivation of an algebra \(A\) over \(k\), and gives a one-to-one correspondence between the set of all pseudo-derivations of \(A\), and the set of all \(p\)-unipotent automorphisms of \(A\). The author also classifies \(p\)-unipotent triangular automorphisms of a polynomial ring \(k[x,y,z]\) in three variables over \(k\) up to conjugation of automorphisms of \(k[x,y,z]\). Another result in the paper is that if a \(p\)-cyclic group \(\mathbb Z_p\) acts triangularly on the polynomial ring \(k[x,y,z]\), then the modular invariant ring \(k[x,y,z]^{\mathbb Z_p}\) is a hypersurface ring.