2007
DOI: 10.12988/ija.2007.07023
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Jordan generalized derivations on \sigma-prime rings

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Cited by 12 publications
(14 citation statements)
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“…Every prime ring with an involution is prime but the converse need not hold general. An example due to Oukhtite [7] justifies the above statement. That is, let R be a prime ring, S D R R o where R o is the opposite ring of R: Define involution on S as .x; y/ D .y; x/: S is prime, but not prime.…”
supporting
confidence: 59%
See 1 more Smart Citation
“…Every prime ring with an involution is prime but the converse need not hold general. An example due to Oukhtite [7] justifies the above statement. That is, let R be a prime ring, S D R R o where R o is the opposite ring of R: Define involution on S as .x; y/ D .y; x/: S is prime, but not prime.…”
supporting
confidence: 59%
“…Therefore any investigation from algebraic point of view might be interesting. Recently, some well-known results concerning prime rings have been proved for prime ring by Oukhtite et al (see, [5][6][7][8][9], where further references can be found). In [1] the authors explored the commutativity of the ring R satisfying one of the following conditions:…”
mentioning
confidence: 99%
“…We define the set which are known as the set of symmetric and skew symmetric elements of R. Let U be a Lie ideal of R. We define which we shall call the centralizer of U with respect to R. Oukhtite and Salhi [12] worked on left derivation on -prime rings and proved that or , where U is a nonzero -square closed Lie ideal of R. Oukhtite and Salhi [12] described additive mappings such that , where U is a nonzero -square closed Lie ideal of a 2-torsion free -prime ring R and prove that for all . Afterwords, Oukhtite, Salhi and Taoufiq [11] studied Jordan generalized derivations on -prime rings and proved that every Jordan generalized derivation on U of R is a generalized derivation on U of R, where U is a -square closed Lie ideal of a 2-torsion free -prime ring R. Some significant results on Lie ideals and generalized derivations in -prime rings have been obtained by M. S. Khan and M. A. Khan [5]. On the other hand, various remarkable characterizations of -prime rings on -square closed Lie ideals have been studied by many authors viz.…”
Section: Introductionmentioning
confidence: 99%
“…During the past few decades, there has been an ongoing interest concerning the relationship between the commutativity of a ring and the behavior of a special mapping on the ring. An example due to Oukhtite [9], shows that every prime ring can be injected in σ-prime ring and from this point of view σ-prime rings constitute a more general class of prime rings. Recently, a major breakthrough has been achieved by Oukhtite et al [10], where the important results by Posner [12], Herstein [5] and Bell [2] have been proved for σ-prime rings.…”
Section: Introductionmentioning
confidence: 99%