Displaying similar documents to “Minimal prime ideals of skew polynomial rings and near pseudo-valuation rings”

Conditions under which R ( x ) and R 〈 x 〉 are almost Q-rings

Hani A. Khashan, H. Al-Ezeh (2007)

Archivum Mathematicum

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All rings considered in this paper are assumed to be commutative with identities. A ring R is a Q -ring if every ideal of R is a finite product of primary ideals. An almost Q -ring is a ring whose localization at every prime ideal is a Q -ring. In this paper, we first prove that the statements, R is an almost Z P I -ring and R [ x ] is an almost Q -ring are equivalent for any ring R . Then we prove that under the condition that every prime ideal of R ( x ) is an extension of a prime ideal of R , the ring R ...

Derivations with Engel conditions in prime and semiprime rings

Shuliang Huang (2011)

Czechoslovak Mathematical Journal

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Let R be a prime ring, I a nonzero ideal of R , d a derivation of R and m , n fixed positive integers. (i) If ( d [ x , y ] ) m = [ x , y ] n for all x , y ∈ I , then R is commutative. (ii) If Char R ≠ 2 and [ d ( x ) , d ( y ) ] m = [ x , y ] n for all x , y ∈ I , then R is commutative. Moreover, we also examine the case when R is a semiprime ring.

Derivations with power central values on Lie ideals in prime rings

Basudeb Dhara, Rajendra K. Sharma (2008)

Czechoslovak Mathematical Journal

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Let R be a prime ring of char R ≠ 2 with a nonzero derivation d and let U be its noncentral Lie ideal. If for some fixed integers n 1 ≥ 0 , n 2 ≥ 0 , n 3 ≥ 0 , ( u n 1 [ d ( u ) , u ] u n 2 ) n 3 ∈ Z ( R ) for all u ∈ U , then R satisfies S 4 , the standard identity in four variables.

Pseudo-valuation rings. II

David F. Anderson, Ayman Badawi, David E. Dobbs (2000)

Bollettino dell'Unione Matematica Italiana

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Viene data una condizione sufficiente affinchè un sopra-anello di un anello di pseudo-valutazione (PVR) sia ancora un PVR. Da ciò segue che se R , M è un PVR, allora ogni sopra-anello di R è un PVR se (e soltanto se) R ⁢ u è quasi-locale per ciascun elemento u di M : M . Vari risultati sono dimostrati per un ideale primo di un anello commutativo arbitrario R , avente Z ⁢ R come insieme di zero-divisori. Per esempio, se P è un primo «forte» di R e contiene un elemento non-zero divisore di R , allora P : P è...

Generalized derivations in prime rings and Banach algebras

Asma Ali, Basudeb Dhara, Shahoor Khan (2014)

Discussiones Mathematicae - General Algebra and Applications

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Let R be a prime ring with extended centroid C, F a generalized derivation of R and n ≥ 1, m≥ 1 fixed integers. In this paper we study the situations: 1. ( F ( x ∘ y ) ) m = ( x ∘ y ) ⁿ for all x,y ∈ I, where I is a nonzero ideal of R; 2. (F(x∘y))ⁿ=(x∘y)ⁿ for all x,y ∈ I, where I is a nonzero right ideal of R. Moreover, we also investigate the situation in semiprime rings and Banach algebras.

Automorphisms of completely primary finite rings of characteristic p

Chiteng'a John Chikunji (2008)

Colloquium Mathematicae

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A completely primary ring is a ring R with identity 1 ≠ 0 whose subset of zero-divisors forms the unique maximal ideal . We determine the structure of the group of automorphisms Aut(R) of a completely primary finite ring R of characteristic p, such that if is the Jacobson radical of R, then ³ = (0), ² ≠ (0), the annihilator of coincides with ² and R / ≅ G F ( p r ) , the finite field of p r elements, for any prime p and any positive integer r.