Displaying similar documents to “Families of functions dominated by distributions of C -classes of mappings”

The trivial locus of an analytic map germ

H. Hauser, G. Muller (1989)

Annales de l'institut Fourier

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We prove: For a local analytic family { X s } s ∈ S of analytic space germs there is a largest subspace T in S such that the family is trivial over T . Moreover the reduction of T equals the germ of those points s in S for which X s is isomorphic to the special fibre X 0 .

Classes of Commutative Clean Rings

Wolf Iberkleid, Warren Wm. McGovern (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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Let A be a commutative ring with identity and I an ideal of A . A is said to be I - c l e a n if for every element a ∈ A there is an idempotent e = e 2 ∈ A such that a - e is a unit and a e belongs to I . A filter of ideals, say ℱ , of A is if for each I ∈ ℱ there is a finitely generated ideal J ∈ ℱ such that J ⊆ I . We characterize I -clean rings for the ideals 0 , n ( A ) , J ( A ) , and A , in terms of the frame of multiplicative Noetherian filters of ideals of A , as well as in terms of more classical ring properties.

Improvement of Grauert-Riemenschneider's theorem for a normal surface

Jean Giraud (1982)

Annales de l'institut Fourier

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Let X ˜ be a desingularization of a normal surface X . The group Pic ( X ˜ ) is provided with an order relation L ≫ _ 0 , defined by L . V ≤ 0 for any effective exceptional divisor V . Comparing to the usual order relation we define the ceiling of L which is an exceptional divisor. This notion allows us to improve the usual vanishing theorem and we deduce from it a numerical criterion for rationality and a genus formula for a curve on a normal surface; the difficulty lies in the case of a Weil divisor which...

On n-derivations and Relations between Elements rⁿ-r for Some n

Maciej Maciejewski, Andrzej Prószyński (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

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We find complete sets of generating relations between the elements [r] = rⁿ - r for n = 2 l and for n = 3. One of these relations is the n-derivation property [rs] = rⁿ[s] + s[r], r,s ∈ R.

On extensions of holomorphic functions satisfying a polynomial growth condition on algebraic varieties in 𝐂 n

Jean Erik Björk (1974)

Annales de l'institut Fourier

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Let V be an algebraic variety in C n and when k ≥ 0 is an integer then Pol ( V , k ) denotes all holomorphic functions f ( z ) on V satisfying | f ( z ) | ≤ C f ( 1 + | z | ) k for all z ∈ V and some constant C f . We estimate the least integer ϵ ( V , k ) such that every f ∈ Pol ( V , k ) admits an extension from V into C n by a polynomial P ( z 1 , ... , z n ) , of degree k + ϵ ( V , k ) at most. In particular lim k > ∞ ϵ ( V , k ) is related to cohomology groups with coefficients in coherent analytic sheaves on V . The existence of the finite integer ϵ ( V , k ) is for example an easy consequence of Kodaira’s Vanishing Theorem. ...

Decomposition of finitely generated modules using Fitting ideals

Somayeh Hadjirezaei, Sina Hedayat (2020)

Czechoslovak Mathematical Journal

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Let R be a commutative Noetherian ring and M be a finitely generated R -module. The main result of this paper is to characterize modules whose first nonzero Fitting ideal is a product of maximal ideals of R , in some cases.

Bounds for quotients in rings of formal power series with growth constraints

Vincent Thilliez (2002)

Studia Mathematica

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In rings Γ M of formal power series in several variables whose growth of coefficients is controlled by a suitable sequence M = ( M l ) l ≥ 0 (such as rings of Gevrey series), we find precise estimates for quotients F/Φ, where F and Φ are series in Γ M such that F is divisible by Φ in the usual ring of all power series. We give first a simple proof of the fact that F/Φ belongs also to Γ M , provided Γ M is stable under derivation. By a further development of the method, we obtain the main result of the paper,...