Semiprime rings with bounded indices of nilpotent elements

1990 ◽  
Vol 50 (2) ◽  
pp. 1518-1526 ◽  
Author(s):  
K. I. Beidar ◽  
A. V. Mikhalev
Keyword(s):  
Nilpotent Elements ◽  
Semiprime Rings

Ad-Nilpotent Elements of Skew Index in Semiprime Rings with Involution

2021 ◽  
Author(s):  
Jose Brox ◽  
Esther García ◽  
Miguel Gómez Lozano ◽  
Rubén Muñoz Alcázar ◽  
Guillermo Vera de Salas
Keyword(s):  
Nilpotent Elements ◽  
Semiprime Rings ◽  
Rings With Involution

Ad-nilpotent Elements of Semiprime Rings with Involution

2018 ◽  
Vol 61 (2) ◽  
pp. 318-327
Author(s):  
Tsiu-Kwen Lee
Keyword(s):  
Positive Integer ◽  
Lie Algebra ◽  
Semiprime Ring ◽  
Extended Centroid ◽  
Nilpotent Elements ◽  
Semiprime Rings ◽  
Rings With Involution ◽  
Torsion Free

AbstractLet R be an n!-torsion free semiprime ring with involution * and with extended centroid C, where n > 1 is a positive integer. We characterize a ∊ K, the Lie algebra of skew elements in R, satisfying (ada)n = 0 on K. This generalizes both Martindale and Miers’ theorem and the theorem of Brox et al. In order to prove it we first prove that if a, b ∊ R satisfy (ada)n = adb on R, where either n is even or b = 0, then (a − λ)[(n+1)/2] = 0 for some λ ∊ C.

A Description of Ad-nilpotent Elements in Semiprime Rings with Involution

2021 ◽  
Author(s):  
Jose Brox ◽  
Esther García ◽  
Miguel Gómez Lozano ◽  
Rubén Muñoz Alcázar ◽  
Guillermo Vera de Salas
Keyword(s):  
Nilpotent Elements ◽  
Semiprime Rings ◽  
Rings With Involution

Identities with Generalized Derivations and Automorphisms on Semiprime Rings

2015 ◽  
Vol 2 (1) ◽  
pp. 24-29
Author(s):  
Asma Ali ◽  
◽  
Shahoor Khan ◽  
Khalid Hamdin
Keyword(s):  
Generalized Derivations ◽  
Semiprime Rings

On quasi-radical of near-ring of polynomials

2019 ◽  
Vol 56 (2) ◽  
pp. 252-259
Author(s):  
Ebrahim Hashemi ◽  
Fatemeh Shokuhifar ◽  
Abdollah Alhevaz
Keyword(s):  
Commutative Ring ◽  
Nilpotent Elements ◽  
Ring Of Polynomials

Abstract The intersection of all maximal right ideals of a near-ring N is called the quasi-radical of N. In this paper, first we show that the quasi-radical of the zero-symmetric near-ring of polynomials R0[x] equals to the set of all nilpotent elements of R0[x], when R is a commutative ring with Nil (R)2 = 0. Then we show that the quasi-radical of R0[x] is a subset of the intersection of all maximal left ideals of R0[x]. Also, we give an example to show that for some commutative ring R the quasi-radical of R0[x] coincides with the intersection of all maximal left ideals of R0[x]. Moreover, we prove that the quasi-radical of R0[x] is the greatest quasi-regular (right) ideal of it.

A Note on Differential Identities in Prime and Semiprime Rings

2020 ◽  
pp. 77-83
Author(s):  
Mohammad Shadab Khan ◽  
Mohd Arif Raza ◽  
Nadeemur Rehman
Keyword(s):  
Prime Ring ◽  
Semiprime Ring ◽  
Nonzero Ideal ◽  
Differential Identities ◽  
Standard Identity ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings ◽  
Positive Integers

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 ( r ○ s)(r ○ s) + ( r ○ s) d ( r ○ s)n - d ( r ○ s))m for all r, s ϵ I, then R is commutative. (ii) If (d ( r ○ s)( r ○ s) + ( r ○ s) d ( r ○ s)n - d (r ○ s))m ϵ Z(R) for all r, s ϵ I, then R satisfies s4, the standard identity in four variables. Moreover, we also examine the case when R is a semiprime ring.

Derivations of differentially semiprime rings

2019 ◽  
Vol 12 (05) ◽  
pp. 1950079
Author(s):  
Ahmad Al Khalaf ◽  
Iman Taha ◽  
Orest D. Artemovych ◽  
Abdullah Aljouiiee
Keyword(s):  
Commutative Ring ◽  
Semiprime Ring ◽  
Prime Rings ◽  
Commutative Case ◽  
Lie Ring ◽  
Lie Rings ◽  
Semiprime Rings ◽  
Torsion Free

Earlier D. A. Jordan, C. R. Jordan and D. S. Passman have investigated the properties of Lie rings Der [Formula: see text] of derivations in a commutative differentially prime rings [Formula: see text]. We study Lie rings Der [Formula: see text] in the non-commutative case and prove that if [Formula: see text] is a [Formula: see text]-torsion-free [Formula: see text]-semiprime ring, then [Formula: see text] is a semiprime Lie ring or [Formula: see text] is a commutative ring.

scholarly journals Some results concerning n-σ-centralizing mappings in semiprime rings

2014 ◽  
Vol 3 (1) ◽  
pp. 15-21
Author(s):  
Vincenzo De Filippis ◽  
Basudeb Dhara
Keyword(s):  
Semiprime Rings
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