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

scholarly journals Jordan algebras at Jordan elements of semiprime rings with involution

2016 ◽  
Vol 468 ◽  
pp. 155-181 ◽  
Author(s):  
Jose Brox ◽  
Esther García ◽  
Miguel Gómez Lozano
Keyword(s):  
Jordan Algebras ◽  
Semiprime Rings ◽  
Rings With Involution

On generalized (θ, φ)-derivations in semiprime rings with involution

2012 ◽  
Vol 62 (3) ◽  
Author(s):  
Mohammad Ashraf ◽  
Nadeem-ur-Rehman ◽  
Shakir Ali ◽  
Muzibur Mozumder
Keyword(s):  
Semiprime Ring ◽  
Additive Mapping ◽  
Semiprime Rings ◽  
Rings With Involution ◽  
Torsion Free

AbstractThe main purpose of this paper is to prove the following result: Let R be a 2-torsion free semiprime *-ring. Suppose that θ, φ are endomorphisms of R such that θ is onto. If there exists an additive mapping F: R → R associated with a (θ, φ)-derivation d of R such that F(xx*) = F(x)θ(x*) + φ(x)d(x*) holds for all x ∈ R, then F is a generalized (θ, φ)-derivation. Further, some more related results are obtained.

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

scholarly journals On Maps of Period 2 on Prime and Semiprime Rings

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
H. E. Bell ◽  
M. N. Daif
Keyword(s):  
Generalized Derivations ◽  
Prime Rings ◽  
Period 2 ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings ◽  
Rings With Involution

A mapfof the ringRinto itself is of period 2 iff2x=xfor allx∈R; involutions are much studied examples. We present some commutativity results for semiprime and prime rings with involution, and we study the existence of derivations and generalized derivations of period 2 on prime and semiprime rings.

scholarly journals Additive maps on prime and semiprime rings with involution

2019 ◽  
pp. 1-8 ◽  
Author(s):  
A. Alahmadi ◽  
H. Alhazmi ◽  
S. Ali ◽  
N.A. Dar ◽  
A.N. Khan
Keyword(s):  
Prime And Semiprime Rings ◽  
Semiprime Rings ◽  
Rings With Involution ◽  
Additive Maps
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