Jordan Derivations on Rings

บทคัดย่อ

An additive mapping d : R→R is called a Jordan derivation on a ring R if d(a2) = d(a)a + ad(a) for all a ∈ R. Two general forms of dn(aba) and dn (abc+cba), where a,b,c ∈ R and n ∈ , are established. It is also shown that if d is a Jordan derivation on a commutative ring R and P is a semiprime
ideal or prime ideal of R where R/P is characteristic – free, then d(P) ⊆ P if and only if dn (P) ⊆P for all positive integers n ≥ 2.