Families of functions dominated by distributions of $C$-classes of mappings

Goo Ishikawa

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 ${X_{s}}_{s \in S}$ 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 $a \in A$ there is an idempotent $e = e^{2} \in A$ 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 $I \in ℱ$ there is a finitely generated ideal $J \in ℱ$ such that $J \subseteq I$ . 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 $\tilde{X}$ be a desingularization of a normal surface $X$ . The group Pic $(\tilde{X})$ is provided with an order relation $L \underline{≫} 0$ , defined by $L$ . $V \leq 0$ 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 $k \geq 0$ is an integer then $Pol (V, k)$ denotes all holomorphic functions $f (z)$ on $V$ satisfying $| f (z) | \leq C_{f} (1 + | z |)^{k}$ for all $z \in V$ and some constant $C_{f}$ . We estimate the least integer $ϵ (V, k)$ such that every $f \in Pol (V, k)$ 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 ${lim}_{k > \infty} ϵ (V, k)$ 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 $M = {(M_{l})}_{l \geq 0}$ (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,...

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

The trivial locus of an analytic map germ

Classes of Commutative Clean Rings

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

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

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

Decomposition of finitely generated modules using Fitting ideals

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

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

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