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Let be a 2-torsion free prime ring and let be a Lie ideal of such that for all . In the present paper it is shown that if is an additive mappings of into itself satisfying for all , then for all .
Let be a 2-torsion free prime ring and let be automorphisms of . For any , set . Suppose that is a -derivation defined on . In the present paper it is shown that if satisfies , then either or is commutative if is a nonzero ideal of such that , for all , and commutes with both and , then either or is commutative. if is a nonzero ideal of such that , for all , and commutes with , then is commutative. Finally a related result has been obtain for -derivation....
Let be a prime ring with center and be a nonzero ideal of . In this manuscript, we investigate the action of skew derivation of which acts as a homomorphism or an anti-homomorphism on . Moreover, we provide an example for semiprime case.
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