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Displaying 81 – 100 of 372

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A note on Bézout's theorem

Sławomir Rams, Piotr Tworzewski, Tadeusz Winiarski (2005)

Annales Polonici Mathematici

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.

A note on characterizations of rings of constants with respect to derivations

Piotr Jędrzejewicz (2004)

Colloquium Mathematicae

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.

A Note on Elementary Derivations

Khoury, Joseph (2004)

Serdica Mathematical Journal

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...

A note on formal power series

Xiao-Xiong Gan, Dariusz Bugajewski (2010)

Commentationes Mathematicae Universitatis Carolinae

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 g is convex and balanced which implies that the subset 𝕏 ¯ g consisting of formal power series which can be composed by a formal power series g possesses such properties. We also provide a necessary and sufficient condition for the superposition operator T g to map 𝕏 ¯ g into itself or to map 𝕏 g into...

A note on Frobenius divided modules in mixed characteristics

Pierre Berthelot (2012)

Bulletin de la Société Mathématique de France

If X is a smooth scheme over a perfect field of characteristic p , and if 𝒟 X ( ) is the sheaf of differential operators on X [7], it is well known that giving an action of 𝒟 X ( ) on an 𝒪 X -module is equivalent to giving an infinite sequence of 𝒪 X -modules descending via the iterates of the Frobenius endomorphism of X [5]. We show that this result can be generalized to any infinitesimal deformation f : X S of a smooth morphism in characteristic p , endowed with Frobenius liftings. We also show that it extends to adic...

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