Commuting and Centralizing Mappings in Prime Rings
Copyright policy )Commuting and Centralizing Mappings in Prime Rings
Let R R be a ring. A mapping F : R → R F:R \to R is said to be commuting on R R if [ F ( x ) , x ] = 0 [F(x),x] = 0 holds for all x ∈ R x \in R . The main purpose of this paper is to prove the following result, which generalizes a classical result of E. Posner: Let R R be a prime ring of characteristic not two. Suppose there exists a nonzero derivation D : R → R D:R \to R , such that the mapping x ↦ [ D ( x ) , x ] x \mapsto [D(x),x] is commuting on R R . In this case R R is commutative.
- University of Maribor Slovenia
Prime and semiprime associative rings, jordansko odvajanje, derivation, commuting mapping, Center, normalizer (invariant elements) (associative rings and algebras), notranje odvajanje, Jordan derivation, odvajanje, asociativni kolobarji in algebre, centralizirajoča preslikava, Automorphisms and endomorphisms, mathematics, prakolobar, associative rings and algebras, inner derivation, centralizing derivations, centralizing mapping, prime rings, prime ring, matematika, info:eu-repo/classification/udc/512.552, kolobar, komutirajoča preslikava
Prime and semiprime associative rings, jordansko odvajanje, derivation, commuting mapping, Center, normalizer (invariant elements) (associative rings and algebras), notranje odvajanje, Jordan derivation, odvajanje, asociativni kolobarji in algebre, centralizirajoča preslikava, Automorphisms and endomorphisms, mathematics, prakolobar, associative rings and algebras, inner derivation, centralizing derivations, centralizing mapping, prime rings, prime ring, matematika, info:eu-repo/classification/udc/512.552, kolobar, komutirajoča preslikava
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