2000 Mathematics Subject Classification: 13N15, 13A50, 16W25.We reduce the Nowicki conjecture on Weitzenböck derivations of polynomial algebras to a well known problem of classical invariant theory.
We present a version of Bézout's theorem basing on the intersection theory in complex analytic geometry. Some applications for products of surfaces and curves are also given.
Let A be a commutative algebra without zero divisors over a field k. If A is finitely generated over k, then there exist well known characterizations of all k-subalgebras of A which are rings of constants with respect to k-derivations of A. We show that these characterizations are not valid in the case when the algebra A is not finitely generated over k.
2000 Mathematics Subject Classification: Primary: 14R10. Secondary: 14R20, 13N15.Let R be a UFD containing a field of characteristic 0, and Bm = R[Y1, . . . , Ym] be a polynomial ring over R. It was conjectured in [5] that if D is an R-elementary monomial derivation of B3 such that ker D is a finitely generated R-algebra then the generators of ker D can be chosen to be linear in the Yi ’s. In this paper, we prove that this does not hold for B4. We also investigate R-elementary derivations D of Bm...
In this note we investigate a relationship between the boundary behavior of power series and the composition of formal power series. In particular, we prove that the composition domain of a formal power series is convex and balanced which implies that the subset consisting of formal power series which can be composed by a formal power series possesses such properties. We also provide a necessary and sufficient condition for the superposition operator to map into itself or to map into...
If is a smooth scheme over a perfect field of characteristic , and if is the sheaf of differential operators on [7], it is well known that giving an action of on an -module is equivalent to giving an infinite sequence of -modules descending via the iterates of the Frobenius endomorphism of [5]. We show that this result can be generalized to any infinitesimal deformation of a smooth morphism in characteristic , endowed with Frobenius liftings. We also show that it extends to adic...