### Some Remarks on Differential Identities in Rings

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**Authors:**M. A. RAZA, H. ALHAZMI AND S. ALI

**DOI:**10.46793/KgJMat2102.259R

**Abstract:**

Let 1 < k and m,k ∈ ℤ

^{+}. In this manuscript, we analyse the action of (semi)-prime rings satisfying certain diﬀerential identities on some suitable subset of rings. To be more speciﬁc, we discuss the behaviour of the semiprime ring ℛ satisfying the diﬀerential identities ([d([s,t]

_{m}), [s,t]

_{m}])

^{k}= [d([s,t]

_{m}), [s,t]

_{m}] for every s,t ∈ℛ.

**Keywords:**

(Semi)-prime ring, derivation, Engel polynomial, maximal right ring of quotients, generalized polynomial identity (GPI).

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