Rendiconti del Seminario Matematico della Università di Padova
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Published online: 2011-06-30
Commutativity of *-Prime Rings with Generalized DerivationsMohammad Ashraf and Almas Khan (1) Aligarh Muslim University, India
(2) Aligarh Muslim University, 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