A Note on Differential Identities in Prime and Semiprime Rings
DOI:
https://doi.org/10.37256/cm.122020127Keywords:
Prime and semiprime rings, Derivations, Martindale ring of quotientsAbstract
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.
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Published
2020-03-23
How to Cite
1.
Mohammad Shadab Khan, Mohd Arif Raza, Rehman N. A Note on Differential Identities in Prime and Semiprime Rings. Contemp. Math. [Internet]. 2020 Mar. 23 [cited 2024 Dec. 11];1(2):77-83. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/127
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Research Article