Displaying similar documents to “Actions of the additive group G a on certain noncommutative deformations of the plane”

The fundamental theorem of prehomogeneous vector spaces modulo p m (With an appendix by F. Sato)

Raf Cluckers, Adriaan Herremans (2007)

Bulletin de la Société Mathématique de France

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For a number field K with ring of integers 𝒪 K , we prove an analogue over finite rings of the form 𝒪 K / 𝒫 m of the fundamental theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where 𝒫 is a big enough prime ideal of 𝒪 K and m > 1 . In the appendix, F.Sato gives an application of the Theorems 1.1, 1.3 and the Theorems A, B, C in J.Denef and A.Gyoja [, Compos. Math., (1998), 237–346] to the functional equation of L -functions of Dirichlet type associated with prehomogeneous...

Further characterizations of Sobolev spaces

Hoai-Minh Nguyen (2008)

Journal of the European Mathematical Society

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Let ( F n ) n be a sequence of non-decreasing functions from [ 0 , + ) into [ 0 , + ) . Under some suitable hypotheses of ( F n ) n , we will prove that if g L p ( N ) , 1 < p < + , satisfies lim inf n N N F n ( | g ( x ) - g ( y ) | ) / | x - y | N + p d x d y < + , then g W 1 , p ( N ) and moreover lim n N N F n ( | g ( x ) - g ( y ) | ) / | x - y | N + p d x d y = K N , p N | g ( x ) | p d x , where K N , p is a positive constant depending only on N and p . This extends some results in J. Bourgain and H-M. Nguyen [A new characterization of Sobolev spaces, C. R. Acad Sci. Paris, Ser. 343 (2006) 75-80] and H-M. Nguyen [Some new characterizations of Sobolev spaces, J. Funct. Anal. 237 (2006) 689-720]. We also present some...

Coxeter elements for vanishing cycles of types  A 1 2  and  D 1 2

Kyoji Saito (2011)

Annales de l’institut Fourier

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We introduce two entire functions f A 1 2 and f D 1 2 in two variables. Both of them have only two critical values 0 and 1 , and the associated maps C 2 C define topologically locally trivial fibrations over C { 0 , 1 } . All critical points in the singular fibers over 0 and 1 are ordinary double points, and the associated vanishing cycles span the middle homology group of the general fiber, whose intersection diagram forms bi-partitely decomposed infinite quivers of type A 1 2 and D 1 2 , respectively. Coxeter elements...

The clean elements of the ring ( L )

Ali Akbar Estaji, Maryam Taha (2024)

Czechoslovak Mathematical Journal

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We characterize clean elements of ( L ) and show that α ( L ) is clean if and only if there exists a clopen sublocale U in L such that 𝔠 L ( coz ( α - 1 ) ) U 𝔬 L ( coz ( α ) ) . Also, we prove that ( L ) is clean if and only if ( L ) has a clean prime ideal. Then, according to the results about ( L ) , we immediately get results about 𝒞 c ( L ) .

Automorphisms and generalized skew derivations which are strong commutativity preserving on polynomials in prime and semiprime rings

Vincenzo de Filippis (2016)

Czechoslovak Mathematical Journal

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Let R be a prime ring of characteristic different from 2, Q r its right Martindale quotient ring and C its extended centroid. Suppose that F , G are generalized skew derivations of R with the same associated automorphism α , and p ( x 1 , ... , x n ) is a non-central polynomial over C such that [ F ( x ) , α ( y ) ] = G ( [ x , y ] ) for all x , y { p ( r 1 , ... , r n ) : r 1 , ... , r n R } . Then there exists λ C such that F ( x ) = G ( x ) = λ α ( x ) for all x R .

Annihilators of skew derivations with Engel conditions on prime rings

Taylan Pehlivan, Emine Albas (2020)

Czechoslovak Mathematical Journal

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Let R be a noncommutative prime ring of characteristic different from 2, with its two-sided Martindale quotient ring Q , C the extended centroid of R and a R . Suppose that δ is a nonzero σ -derivation of R such that a [ δ ( x n ) , x n ] k = 0 for all x R , where σ is an automorphism of R , n and k are fixed positive integers. Then a = 0 .

( φ , ϕ ) -derivations on semiprime rings and Banach algebras

Bilal Ahmad Wani (2021)

Communications in Mathematics

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Let be a semiprime ring with unity e and φ , ϕ be automorphisms of . In this paper it is shown that if satisfies 2 𝒟 ( x n ) = 𝒟 ( x n - 1 ) φ ( x ) + ϕ ( x n - 1 ) 𝒟 ( x ) + 𝒟 ( x ) φ ( x n - 1 ) + ϕ ( x ) 𝒟 ( x n - 1 ) for all x and some fixed integer n 2 , then 𝒟 is an ( φ , ϕ )-derivation. Moreover, this result makes it possible to prove that if admits an additive mappings 𝒟 , 𝒢 : satisfying the relations 2 𝒟 ( x n ) = 𝒟 ( x n - 1 ) φ ( x ) + ϕ ( x n - 1 ) 𝒢 ( x ) + 𝒢 ( x ) φ ( x n - 1 ) + ϕ ( x ) 𝒢 ( x n - 1 ) , 2 𝒢 ( x n ) = 𝒢 ( x n - 1 ) φ ( x ) + ϕ ( x n - 1 ) 𝒟 ( x ) + 𝒟 ( x ) φ ( x n - 1 ) + ϕ ( x ) 𝒟 ( x n - 1 ) , for all x and some fixed integer n 2 , then 𝒟 and 𝒢 are ( φ , ϕ )derivations under some torsion restriction. Finally, we apply these purely ring theoretic results to semi-simple Banach algebras. ...

Annihilating and power-commuting generalized skew derivations on Lie ideals in prime rings

Vincenzo de Filippis (2016)

Czechoslovak Mathematical Journal

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Let R be a prime ring of characteristic different from 2 and 3, Q r its right Martindale quotient ring, C its extended centroid, L a non-central Lie ideal of R and n 1 a fixed positive integer. Let α be an automorphism of the ring R . An additive map D : R R is called an α -derivation (or a skew derivation) on R if D ( x y ) = D ( x ) y + α ( x ) D ( y ) for all x , y R . An additive mapping F : R R is called a generalized α -derivation (or a generalized skew derivation) on R if there exists a skew derivation D on R such that F ( x y ) = F ( x ) y + α ( x ) D ( y ) for all x , y R . We prove...

Generalized reverse derivations and commutativity of prime rings

Shuliang Huang (2019)

Communications in Mathematics

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Let R be a prime ring with center Z ( R ) and I a nonzero right ideal of R . Suppose that R admits a generalized reverse derivation ( F , d ) such that d ( Z ( R ) ) 0 . In the present paper, we shall prove that if one of the following conditions holds: (i) F ( x y ) ± x y Z ( R ) , (ii) F ( [ x , y ] ) ± [ F ( x ) , y ] Z ( R ) , (iii) F ( [ x , y ] ) ± [ F ( x ) , F ( y ) ] Z ( R ) , (iv) F ( x y ) ± F ( x ) F ( y ) Z ( R ) , (v) [ F ( x ) , y ] ± [ x , F ( y ) ] Z ( R ) , (vi) F ( x ) y ± x F ( y ) Z ( R ) for all x , y I , then R is commutative.

Green functions, Segre numbers, and King’s formula

Mats Andersson, Elizabeth Wulcan (2014)

Annales de l’institut Fourier

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Let 𝒥 be a coherent ideal sheaf on a complex manifold X with zero set Z , and let G be a plurisubharmonic function such that G = log | f | + 𝒪 ( 1 ) locally at Z , where f is a tuple of holomorphic functions that defines 𝒥 . We give a meaning to the Monge-Ampère products ( d d c G ) k for k = 0 , 1 , 2 , ... , and prove that the Lelong numbers of the currents M k 𝒥 : = 1 Z ( d d c G ) k at x coincide with the so-called Segre numbers of J at x , introduced independently by Tworzewski, Gaffney-Gassler, and Achilles-Manaresi. More generally, we show that M k 𝒥 satisfy a certain...