Original scientific paper

On commutativity of σ-prime rings

L. Oukhtite
S. Salhi

Abstract

Let R be a 2-torsion free σ-prime ring having a σ-square closed Lie ideal U and an automorphism T centralizing on U. We prove that if there exists u0 in Saσ(R) with Ru0 ⊂ U and if T commutes with σ on U, then U is contained in the center of R. This result is then applied to generalize the result of J. Mayne for centralizing automorphisms to σ-prime rings. Finally, for a 2-torsion free σ-prime ring possessing a nonzero derivation, we give suitable conditions under which the ring must be commutative.

Keywords

Rings with involution; σ-prime rings; centralizing automorphisms; square closed Lie ideals; derivations; commutativity

Hrčak ID:

3298

URI

https://hrcak.srce.hr/3298

Publication date:

24.5.2006.

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