Displaying similar documents to “Essential $P$-spaces: a generalization of door spaces”

Equations in the Hadamard ring of rational functions

Andrea Ferretti, Umberto Zannier (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let K be a number field. It is well known that the set of recurrencesequences with entries in K is closed under component-wise operations, and so it can be equipped with a ring structure. We try to understand the structure of this ring, in particular to understand which algebraic equations have a solution in the ring. For the case of cyclic equations a conjecture due to Pisot states the following: assume { a n } is a recurrence sequence and suppose that all the a n have a d th root in the field...

(Generalized) filter properties of the amalgamated algebra

Yusof Azimi (2022)

Archivum Mathematicum

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Let R and S be commutative rings with unity, f : R S a ring homomorphism and J an ideal of S . Then the subring R f J : = { ( a , f ( a ) + j ) a R and j J } of R × S is called the amalgamation of R with S along J with respect to f . In this paper, we determine when R f J is a (generalized) filter ring.

Correct solvability of a general differential equation of the first order in the space L p ( )

Nina A. Chernyavskaya, Leonid A. Shuster (2015)

Archivum Mathematicum

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We consider the equation - r ( x ) y ' ( x ) + q ( x ) y ( x ) = f ( x ) , x where f L p ( ) , p [ 1 , ] ( L ( ) : = C ( ) ) and 0 < r C ( ) , 0 q L 1 ( ) . We obtain minimal requirements to the functions r and q , in addition to (), under which equation () is correctly solvable in L p ( ) , p [ 1 , ] .

On minimal ideals in the ring of real-valued continuous functions on a frame

Abolghasem Karimi Feizabadi, Ali Akbar Estaji, Mostafa Abedi (2018)

Archivum Mathematicum

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Let L be the ring of real-valued continuous functions on a frame L . The aim of this paper is to study the relation between minimality of ideals I of L and the set of all zero sets in L determined by elements of I . To do this, the concepts of coz-disjointness, coz-spatiality and coz-density are introduced. In the case of a coz-dense frame L , it is proved that the f -ring L is isomorphic to the f -ring C ( Σ L ) of all real continuous functions on the topological space Σ L . Finally, a one-one correspondence...

( 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. ...

P-injective group rings

Liang Shen (2020)

Czechoslovak Mathematical Journal

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A ring R is called right P-injective if every homomorphism from a principal right ideal of R to R R can be extended to a homomorphism from R R to R R . Let R be a ring and G a group. Based on a result of Nicholson and Yousif, we prove that the group ring RG is right P-injective if and only if (a) R is right P-injective; (b) G is locally finite; and (c) for any finite subgroup H of G and any principal right ideal I of RH , if f Hom R ( I R , R R ) , then there exists g Hom R ( RH R , R R ) such that g | I = f . Similarly, we also obtain equivalent...

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...

Symmetric and reversible properties of bi-amalgamated rings

Antonysamy Aruldoss, Chelliah Selvaraj (2024)

Czechoslovak Mathematical Journal

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Let f : A B and g : A C be two ring homomorphisms and let K and K ' be two ideals of B and C , respectively, such that f - 1 ( K ) = g - 1 ( K ' ) . We investigate unipotent, symmetric and reversible properties of the bi-amalgamation ring A f , g ( K , K ' ) of A with ( B , C ) along ( K , K ' ) with respect to ( f , g ) .

Strongly 2-nil-clean rings with involutions

Huanyin Chen, Marjan Sheibani Abdolyousefi (2019)

Czechoslovak Mathematical Journal

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A * -ring R is strongly 2-nil- * -clean if every element in R is the sum of two projections and a nilpotent that commute. Fundamental properties of such * -rings are obtained. We prove that a * -ring R is strongly 2-nil- * -clean if and only if for all a R , a 2 R is strongly nil- * -clean, if and only if for any a R there exists a * -tripotent e R such that a - e R is nilpotent and e a = a e , if and only if R is a strongly * -clean SN ring, if and only if R is abelian, J ( R ) is nil and R / J ( R ) is * -tripotent. Furthermore, we explore...