Jordan left *-centralizers of prime and semiprime rings with involution

2012 ◽  
Vol 54 (2) ◽  
pp. 609-624 ◽  
Author(s):  
Shakir Ali ◽  
Nadeem Ahmad Dar ◽  
Joso Vukman
Keyword(s):  
Prime And Semiprime Rings ◽  
Semiprime Rings ◽  
Rings With Involution

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

scholarly journals A note on Jordan left *-centralizers on prime and semiprime rings with involution

2017 ◽  
Vol 11 (6) ◽  
pp. 1080-1082
Author(s):  
M.S. Tammam El-Sayiad ◽  
N.M. Muthana ◽  
Z.S. Alkhamisi
Keyword(s):  
Prime And Semiprime Rings ◽  
Semiprime Rings ◽  
Rings With Involution

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.

Annihilator condition of a pair of derivations in prime and semiprime rings

2016 ◽  
Vol 47 (1) ◽  
pp. 111-124 ◽  
Author(s):  
Basudeb Dhara ◽  
Nurcan Argaç ◽  
Krishna Gopal Pradhan
Keyword(s):  
Prime And Semiprime Rings ◽  
Semiprime Rings

scholarly journals Generalized Derivations on Power Values of Lie Ideals in Prime and Semiprime Rings

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Vincenzo De Filippis ◽  
Nadeem UR Rehman ◽  
Abu Zaid Ansari
Keyword(s):  
Lie Ideal ◽  
Generalized Derivations ◽  
Fixed Integer ◽  
Free Ring ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings ◽  
Positive Integers ◽  
Torsion Free

LetRbe a 2-torsion free ring and letLbe a noncentral Lie ideal ofR, and letF:R→RandG:R→Rbe two generalized derivations ofR. We will analyse the structure ofRin the following cases: (a)Ris prime andF(um)=G(un)for allu∈Land fixed positive integersm≠n; (b)Ris prime andF((upvq)m)=G((vrus)n)for allu,v∈Land fixed integersm,n,p,q,r,s≥1; (c)Ris semiprime andF((uv)n)=G((vu)n)for allu,v∈[R,R]and fixed integern≥1; and (d)Ris semiprime andF((uv)n)=G((vu)n)for allu,v∈Rand fixed integern≥1.

Semi-Prime Modules

1966 ◽  
Vol 18 ◽  
pp. 823-831 ◽  
Author(s):  
E. H. Feller ◽  
E. W. Swokowski
Keyword(s):  
Prime Rings ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings

Properties and characterizations for prime and semiprime rings have been provided by A. W. Goldie (2, 3). In a previous paper (1), the authors used the results of (2) to characterize prime and uniform prime modules. It is the aim of the present paper to generalize Goldie's work on semi-prime rings (3) to modules. In this setting certain new properties will appear.Notationally, in the work to follow, the symbol R always denotes a ring and all R-modules will be right R-modules.In the theory of rings an ideal C is said to be prime if and only if whenever AB ⊆ C for ideals A and B, then either A ⊆ C or B ⊆ C. A ring is prime if the zero ideal is prime.

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