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- W2184054920 abstract "Let R be a ring and �,� be automorphisms of R. An additive mapping F: R → R is called a generalized (�,�)-derivation on R if there exists an (�,�)- derivation d: R → R such that F(xy) = F(x)�(y) + �(x)d(y) holds for all x,y ∈ R. For any x,y ∈ R, set (x,y)�,� = x�(y) − �(y)x and (x ◦ y)�,� = x�(y) + �(y)x. In the present paper, we shall discuss the commutativity of a prime ring R admitting generalized (�,�)-derivations F and G satisfying any one of the following properties: (i) F((x,y)) = (x ◦ y)�,�, (ii) F(x ◦ y) = (x,y)�,�, (iii) (F(x),y)�,� = (F(x) ◦ y)�,�, (iv) F((x,y)) = (F(x),y)�,�, (v) F(x ◦ y) = (F(x) ◦ y)�,�, (vi) F((x,y) = (�(x),G(y)) and (vii) F(x ◦ y) = (�(x) ◦ G(y)) for all x,y in some appropriate subset of R. Finally, obtain some results on semi-projective Morita context with generalized (�,�)-derivations." @default.
- W2184054920 created "2016-06-24" @default.
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- W2184054920 date "2009-01-01" @default.
- W2184054920 modified "2023-09-27" @default.
- W2184054920 title "On Lie Structure of Prime Rings with Generalized (,)-Derivations" @default.
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