Results 61 to 70 of about 184 (133)
A Commutativity theorem for semiprime rings [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1980 AbstractIt is shown that if R is a semiprime ring with 1 satisfying the property that, for each x, y ∈ R, there exists a positive integer n depending on x and y such that (xy)k − xkyk is central for k = n,n+1, n+2, then R is commutative, thus generalizing a result of Kaya.
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A Study of Generalized Differential Identities via Prime Ideals
Journal of Mathematics, Volume 2025, Issue 1, 2025.Let R be a ring and P be a prime ideal of R. The aim of this research paper is to delve into the relationship between the structural properties of the quotient ring R/P and the behavior of generalized derivations in a ring R endowed with an involution.
Ali Yahya Hummdi +4 more
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Jordan ?-Centralizers of Prime and Semiprime Rings
مجلة بغداد للعلوم, 2010 The purpose of this paper is to prove the following result: Let R be a 2-torsion free ring and T: R?R an additive mapping such that T is left (right) Jordan ?-centralizers on R.
Baghdad Science Journal
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On semiprime segments of rings [PDF]
Journal of the Australian Mathematical Society, 2006 AbstractA semiprime segment of a ring R is a pair P2 ⊂ P1 of semiprime ideals of R such that ∩ In ⊆ P2 for all ideals I of R with P2 ⊂ I ⊂ P1. In this paper semiprime segments with P1 a comparizer ideal are classified as either simple, exceptional, or archimedean, extending to several classes of rings a classification known for right chain rings. These
Mazurek, R., Törner, G.
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Modules With Epimorphisms Between Their Submodules
Journal of Mathematics, Volume 2025, Issue 1, 2025.An R‐module M is called weakly uniserial if its submodules are comparable regarding embedding, i.e., if for any two submodules N, K of M, HomR(N, K) or HomR(K, N) contains an injective element. Here, we are interested in studying modules which for any two submodules of them there is an epimorphism from one to the other.
P. Karimi Beiranvand, Pramita Mishra
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Some Results of Prime And Semiprime Rings With Derivations
مجلة بغداد للعلوم, 2005 The main purpose of this paper is to study prime and semiprime rings admitting a derivation d satisfying new conditions when d acts as homomorphism on non-zero ideal.
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COMMUTING AND 2-COMMUTING DERIVATIONS OF SEMIPRIME RINGS
Journal of Kufa for Mathematics and Computer, 2012 The main purpose of this paper is to study and investigate some results concerning generalized derivation D on semiprime ring R, we obtain a derivation d is commuting and 2-commuting on R.
Mehsin Jabel Atteya +1 more
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A NOTE ON CENTRALIZERS IN SEMIPRIME RINGS
Demonstratio Mathematica, 2005 Summary: The purpose of this paper is to prove the following result: Let \(R\) be a \((m+n+2)!\) and \(3m^2n+3mn^2+4m^2+4n^2+10mn\)-torsion free semiprime ring with an identity element and let \(T\colon R\to R\) be an additive mapping such that \[ 3T(x^{m+n+1})=T(x)x^{m+n}+x^mT(x)x^n+x^{m+n}T(x) \] is fulfilled for all \(x\in R\) and some fixed ...
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Higher Derivations Satisfying Certain Identities in Rings
Journal of Mathematics, Volume 2024, Issue 1, 2024.Let n and m be fixed positive integers. In this paper, we establish some structural properties of prime rings equipped with higher derivations. Motivated by the works of Herstein and Bell‐Daif, we characterize rings with higher derivations D=dii∈N satisfying (i) dnx,dmy∈ZR for all x,y∈R and (ii) dnx,y∈ZR for all x,y∈R.
Amal S. Alali +4 more
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Derivations of higher order in semiprime rings
International Journal of Mathematics and Mathematical Sciences, 1998 Let R be a 2-torsion free semiprime ring with derivation d. Supposed d2n is a derivation of R, where n is a positive integer. It is shown that if R is (4n−2)-torsion free or if R is an inner derivation of R, then d2n−1=0.
Jiang Luh, Youpei Ye
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