# Generalized Derivations on ∗-prime Rings

• Ashraf, Mohammad (Department of Mathematics, Aligarh Muslim University) ;
• Jamal, Malik Rashid (Department of Mathematics, Integral University)
• Accepted : 2018.08.20
• Published : 2018.09.23
• 123 7

#### Abstract

Let I be a ${\ast}$-ideal on a 2-torsion free ${\ast}$-prime ring and $F:R{\rightarrow}R$ a generalized derivation with an associated derivation $d:R{\rightarrow}R$. The aim of this paper is to explore the condition under which generalized derivation F becomes a left centralizer i.e., associated derivation d becomes a trivial map (i.e., zero map) on R.

#### Keywords

derivation;generalized derivation;${\ast}$-prime ring;centralizer

#### References

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