Displaying similar documents to “An elementary proof of the Briançon-Skoda theorem”

On a generalization of de Rham lemma

Kyoji Saito (1976)

Annales de l'institut Fourier

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Let M be a free module over a noetherian ring. For ω 1 , ... , ω k M , let 𝒜 be the ideal generated by coefficients of ω 1 ... ω k . For an element ω p M with p < prof . 𝒜 , if ω ω 1 ... ω k = 0 , there exists η 1 , ... , η k p - 1 M such that ω = i = 1 k η i ω i . This is a generalization of a lemma on the division of forms due to de Rham (Comment. Math. Helv., 28 (1954)) and has some applications to the study of singularities.

On the Noether exponent

Anna Stasica (2003)

Annales Polonici Mathematici

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We obtain, in a simple way, an estimate for the Noether exponent of an ideal I without embedded components (i.e. we estimate the smallest number μ such that ( r a d I ) μ I ).

A result on extension of C.R. functions

Makhlouf Derridj, John Erik Fornaess (1983)

Annales de l'institut Fourier

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Let Ω an open set in C 4 near z 0 Ω , λ a suitable holomorphic function near z 0 . If we know that we can solve the following problem (see [M. Derridj, Annali. Sci. Norm. Pisa, Série IV, vol. IX (1981)]) : u = λ f , ( f is a ( 0 , 1 ) form, closed in U ( z 0 ) in U ( z 0 ) with supp ( u ) Ω U ( z 0 ) , then we deduce an extension result for C . R . functions on Ω U ( z 0 ) , as holomorphic fonctions in Ω V ( z 0 ) .

Unique continuation for the solutions of the laplacian plus a drift

Alberto Ruiz, Luis Vega (1991)

Annales de l'institut Fourier

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We prove unique continuation for solutions of the inequality | Δ u ( x ) | V ( x ) | u ( x ) | , x Ω a connected set contained in R n and V is in the Morrey spaces F α , p , with p ( n - 2 ) / 2 ( 1 - α ) and α < 1 . These spaces include L q for q ( 3 n - 2 ) / 2 (see [H], [BKRS]). If p = ( n - 2 ) / 2 ( 1 - α ) , the extra assumption of V being small enough is needed.

C(X) vs. C(X) modulo its socle

F. Azarpanah, O. A. S. Karamzadeh, S. Rahmati (2008)

Colloquium Mathematicae

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Let C F ( X ) be the socle of C(X). It is shown that each prime ideal in C ( X ) / C F ( X ) is essential. For each h ∈ C(X), we prove that every prime ideal (resp. z-ideal) of C(X)/(h) is essential if and only if the set Z(h) of zeros of h contains no isolated points (resp. int Z(h) = ∅). It is proved that d i m ( C ( X ) / C F ( X ) ) d i m C ( X ) , where dim C(X) denotes the Goldie dimension of C(X), and the inequality may be strict. We also give an algebraic characterization of compact spaces with at most a countable number of nonisolated points....

Sets in N with vanishing global extremal function and polynomial approximation

Józef Siciak (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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Let Γ be a non-pluripolar set in N . Let f be a function holomorphic in a connected open neighborhood G of Γ . Let { P n } be a sequence of polynomials with deg P n d n ( d n < d n + 1 ) such that lim sup n | f ( z ) - P n ( z ) | 1 / d n < 1 , z Γ . We show that if lim sup n | P n ( z ) | 1 / d n 1 , z E , where E is a set in N such that the global extremal function V E 0 in N , then the maximal domain of existence G f of f is one-sheeted, and lim sup n f - P n K 1 d n < 1 for every compact set K G f . If, moreover, the sequence { d n + 1 / d n } is bounded then G f = N . If E is a closed...

On wsq-primary ideals

Emel Aslankarayiğit Uğurlu, El Mehdi Bouba, Ünsal Tekir, Suat Koç (2023)

Czechoslovak Mathematical Journal

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We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let R be a commutative ring with a nonzero identity and Q a proper ideal of R . The proper ideal Q is said to be a weakly strongly quasi-primary ideal if whenever 0 a b Q for some a , b R , then a 2 Q or b Q . Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero...