Automorphisms and derivations in prime rings

Abstract

Let R be a non-commutative ring, I a non-zero two-sided ideal of R and f a mapping on R such that f([x, y])−[x, y] is zero or invertible for every x, y ∈ I. If R is a prime ring and f a non-trivial automorphism or a non-zero derivation on R then either R = D or R = M_2(D), the ring of all 2 × 2 matrices over D, where D is a division ring. Moreover we will examine the case when R is a semiprime ring and f a non-zero derivation of R.

Keywords

• prime and semiprime rings
• derivations
• differential identities