| Abstrakt: |
Let R be a ring, P a semiprime ideal of R. A map F: R → R is called a multiplicative generalized derivation if there exists a map d: R → R such that F(xy) = F(x)y + xd(y), for all x, y ∈ R. Then, d is P-commuting map on R, if R admits a multiplicative generalized derivation F associated with a nonzero map d such that: (i) [F(x), x] ∈ P, (ii) F(x) ◦ x ∈ P, (iii)F([x, y]) ∈ P,(iv) F(xoy) ∈ P,(v) F([x, y]) ± [G(x), y] ∈ P, (vi)F(xoy) ± (G(x)oy) ∈ P, (vii)[F(x), y] ± [x,G(y)] ∈ P, (viii)F([x, y]) ± (G(x)oy) ∈ P,(ix)F(xoy) ± [G(x), y] ∈ P, (x) F(x)oy ± xoG(y) ∈ P, (xi) F(x)F(y) ± [x, y] ∈ P, (xii) F(x)F(y) ± (x ◦ y) ∈ P, ∀x, y ∈ R [ABSTRACT FROM AUTHOR] |
