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

Similarity:

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

Similarity:

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

Similarity:

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

Similarity:

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

Similarity:

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

Similarity:

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...

Some generalizations of Olivier's theorem

Alain Faisant, Georges Grekos, Ladislav Mišík (2016)

Mathematica Bohemica

Similarity:

Let n = 1 a n be a convergent series of positive real numbers. L. Olivier proved that if the sequence ( a n ) is non-increasing, then lim n n a n = 0 . In the present paper: (a) We formulate and prove a necessary and sufficient condition for having lim n n a n = 0 ; Olivier’s theorem is a consequence of our Theorem . (b) We prove properties analogous to Olivier’s property when the usual convergence is replaced by the -convergence, that is a convergence according to an ideal of subsets of . Again, Olivier’s theorem is a consequence...

More on the strongly 1-absorbing primary ideals of commutative rings

Ali Yassine, Mohammad Javad Nikmehr, Reza Nikandish (2024)

Czechoslovak Mathematical Journal

Similarity:

Let R be a commutative ring with identity. We study the concept of strongly 1-absorbing primary ideals which is a generalization of n -ideals and a subclass of 1 -absorbing primary ideals. A proper ideal I of R is called strongly 1-absorbing primary if for all nonunit elements a , b , c R such that a b c I , it is either a b I or c 0 . Some properties of strongly 1-absorbing primary ideals are studied. Finally, rings R over which every semi-primary ideal is strongly 1-absorbing primary, and rings R over which...