Displaying similar documents to “Automorphisms and derivations of a Fréchet algebra of locally integrable functions”

On automorphisms of the Banach space / c

Piotr Koszmider, Cristóbal Rodríguez-Porras (2016)

Fundamenta Mathematicae

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We investigate Banach space automorphisms T : / c / c focusing on the possibility of representing their fragments of the form T B , A : ( A ) / c ( A ) ( B ) / c ( B ) for A,B ⊆ ℕ infinite by means of linear operators from ( A ) into ( B ) , infinite A×B-matrices, continuous maps from B* = βB∖B into A*, or bijections from B to A. This leads to the analysis of general bounded linear operators on / c . We present many examples, introduce and investigate several classes of operators, for some of them we obtain satisfactory representations and for...

Polycyclic groups with automorphisms of order four

Tao Xu, Fang Zhou, Heguo Liu (2016)

Czechoslovak Mathematical Journal

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In this paper, we study the structure of polycyclic groups admitting an automorphism of order four on the basis of Neumann’s result, and prove that if α is an automorphism of order four of a polycyclic group G and the map ϕ : G G defined by g ϕ = [ g , α ] is surjective, then G contains a characteristic subgroup H of finite index such that the second derived subgroup H ' ' is included in the centre of H and C H ( α 2 ) is abelian, both C G ( α 2 ) and G / [ G , α 2 ] are abelian-by-finite. These results extend recent and classical results in...

Coleman automorphisms of finite groups with a self-centralizing normal subgroup

Jinke Hai (2020)

Czechoslovak Mathematical Journal

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Let G be a finite group with a normal subgroup N such that C G ( N ) N . It is shown that under some conditions, Coleman automorphisms of G are inner. Interest in such automorphisms arose from the study of the normalizer problem for integral group rings.

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 .

Automorphisms of metacyclic groups

Haimiao Chen, Yueshan Xiong, Zhongjian Zhu (2018)

Czechoslovak Mathematical Journal

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A metacyclic group H can be presented as α , β : α n = 1 , β m = α t , β α β - 1 = α r for some n , m , t , r . Each endomorphism σ of H is determined by σ ( α ) = α x 1 β y 1 , σ ( β ) = α x 2 β y 2 for some integers x 1 , x 2 , y 1 , y 2 . We give sufficient and necessary conditions on x 1 , x 2 , y 1 , y 2 for σ to be an automorphism.

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 .

Bicrossed products of generalized Taft algebra and group algebras

Dingguo Wang, Xiangdong Cheng, Daowei Lu (2022)

Czechoslovak Mathematical Journal

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Let G be a group generated by a set of finite order elements. We prove that any bicrossed product H m , d ( q ) k [ G ] between the generalized Taft algebra H m , d ( q ) and group algebra k [ G ] is actually the smash product H m , d ( q ) k [ G ] . Then we show that the classification of these smash products could be reduced to the description of the group automorphisms of G . As an application, the classification of H m , d ( q ) k [ C n 1 × C n 2 ] is completely presented by generators and relations, where C n denotes the n -cyclic group.

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...

( 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. ...

A note on Skolem-Noether algebras

Juncheol Han, Tsiu-Kwen Lee, Sangwon Park (2021)

Czechoslovak Mathematical Journal

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The paper was motivated by Kovacs’ paper (1973), Isaacs’ paper (1980) and a recent paper, due to Brešar et al. (2018), concerning Skolem-Noether algebras. Let K be a unital commutative ring, not necessarily a field. Given a unital K -algebra S , where K is contained in the center of S , n , the goal of this paper is to study the question: when can a homomorphism φ : M n ( K ) M n ( S ) be extended to an inner automorphism of M n ( S ) ? As an application of main results presented in the paper, it is proved that if S is...

Equidistribution towards the Green current for holomorphic maps

Tien-Cuong Dinh, Nessim Sibony (2008)

Annales scientifiques de l'École Normale Supérieure

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Let f be a non-invertible holomorphic endomorphism of a projective space and f n its iterate of order n . We prove that the pull-back by f n of a generic (in the Zariski sense) hypersurface, properly normalized, converges to the Green current associated to f when n tends to infinity. We also give an analogous result for the pull-back of positive closed ( 1 , 1 ) -currents and a similar result for regular polynomial automorphisms of  k .

On σ -permutably embedded subgroups of finite groups

Chenchen Cao, Li Zhang, Wenbin Guo (2019)

Czechoslovak Mathematical Journal

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Let σ = { σ i : i I } be some partition of the set of all primes , G be a finite group and σ ( G ) = { σ i : σ i π ( G ) } . A set of subgroups of G is said to be a complete Hall σ -set of G if every non-identity member of is a Hall σ i -subgroup of G and contains exactly one Hall σ i -subgroup of G for every σ i σ ( G ) . G is said to be σ -full if G possesses a complete Hall σ -set. A subgroup H of G is σ -permutable in G if G possesses a complete Hall σ -set such that H A x = A x H for all A and all x G . A subgroup H of G is σ -permutably embedded in...

On the conjugate type vector and the structure of a normal subgroup

Ruifang Chen, Lujun Guo (2022)

Czechoslovak Mathematical Journal

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Let N be a normal subgroup of a group G . The structure of N is given when the G -conjugacy class sizes of N is a set of a special kind. In fact, we give the structure of a normal subgroup N under the assumption that the set of G -conjugacy class sizes of N is ( p 1 n 1 a 1 n 1 , , p 1 1 a 11 , 1 ) × × ( p r n r a r n r , , p r 1 a r 1 , 1 ) , where r > 1 , n i > 1 and p i j are distinct primes for i { 1 , 2 , , r } , j { 1 , 2 , , n i } .

The group of automorphisms of L is algebraically reflexive

Félix Cabello Sánchez (2004)

Studia Mathematica

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We study the reflexivity of the automorphism (and the isometry) group of the Banach algebras L ( μ ) for various measures μ. We prove that if μ is a non-atomic σ-finite measure, then the automorphism group (or the isometry group) of L ( μ ) is [algebraically] reflexive if and only if L ( μ ) is *-isomorphic to L [ 0 , 1 ] . For purely atomic measures, we show that the group of automorphisms (or isometries) of ( Γ ) is reflexive if and only if Γ has non-measurable cardinal. So, for most “practical” purposes, the automorphism...

Selectors of discrete coarse spaces

Igor Protasov (2022)

Commentationes Mathematicae Universitatis Carolinae

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Given a coarse space ( X , ) with the bornology of bounded subsets, we extend the coarse structure from X × X to the natural coarse structure on ( { } ) × ( { } ) and say that a macro-uniform mapping f : ( { } ) X (or f : [ X ] 2 X ) is a selector (or 2-selector) of ( X , ) if f ( A ) A for each A { } ( A [ X ] 2 , respectively). We prove that a discrete coarse space ( X , ) admits a selector if and only if ( X , ) admits a 2-selector if and only if there exists a linear order “ " on X such that the family of intervals { [ a , b ] : a , b X , a b } is a base for the bornology .