@article{Ali2023, 
author = {Shakir Ali and Turki M. Alsuraiheed and Nazia Parveen and Vaishali Varshney},
title = {Action of    n-derivations and    n-multipliers on ideals of (semi)-prime rings},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {7},
pages = {17208-17228},
keywords = {semiprime ring, ideal, derivation, symmetric n-derivation, n-multiplier},
url = {https://www.sciopen.com/article/10.3934/math.2023879},
doi = {10.3934/math.2023879},
abstract = {The present paper aims to investigate the containment of nonzero central ideal in a ring        R   when the trace of symmetric    n-derivations satisfies some differential identities. Lastly, we prove that in a prime ring        R   of suitable torsion restriction, if        D    ,      G    :            R        n    →      R   are two nonzero symmetric    n-derivations such that        f    (  ϑ  )  ϑ  +  ϑ      g    (  ϑ  )  =  0 holds    ∀    ϑ  ∈      W  , a nonzero left ideal of        R   where        f   and        g   are the traces of        D   and        G  , respectively, then either        R   is commutative or        G   acts as a left    n-multiplier. Finally, we characterize symmetric    n-derivations in terms of left    n-multipliers.}
}