A Note on Differential Identities in Prime and Semiprime Rings

Authors

  • Mohammad Shadab Khan Department of Commerce, Aligarh Muslim University, Aligarh-202002, India
  • Mohd Arif Raza Faculty of Science and Arts-Rabigh King Abdulaziz University, Jeddah KSA
  • Nadeemur Rehman Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India

DOI:

https://doi.org/10.37256/cm.122020127

Keywords:

Prime and semiprime rings, Derivations, Martindale ring of quotients

Abstract

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 (rs)(r s) + (rs) d (rs)n - d (rs))m for all r, s ϵ I, then R is commutative. (ii) If (d (rs)(rs) + (rs) d (rs)n - d (rs)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