Rendiconti del Seminario Matematico della Università di Padova
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Commutativity of *-Prime Rings with Generalized DerivationsMohammad Ashraf and Almas Khan (1) Department of Mathematics, Aligarh Muslim University, 202 002, Aligarh, India
(2) Department of Mathematics, Aligarh Muslim University, 202 002, Aligarh, India
Let R be a 2-torsion free ∗-prime ring and F be a generalized derivation of R with associated derivation d. If U is a ∗-Lie ideal of R then in the present paper, we shall show that U ⊆ Z(R) if R admits a generalized derivation F (with associated derivation d) satisfying any one of the properties: (i) F[u,v]=[F(u),v], (ii) F(uov)=F(u)ov, (iii) F[u,v]=[F(u),v]+[d(v),u], (iv) F(uov)=F(u)ov+ d(v)ou, (v) F(uv)±uv=0 and(vi) d(u)F(v)±uv=0 for all u,v ∈ U.
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Ashraf Mohammad, Khan Almas: Commutativity of *-Prime Rings with Generalized Derivations. Rend. Sem. Mat. Univ. Padova 125 (2011), 71-79. doi: 10.4171/RSMUP/125-5