Glasnik Matematicki, Vol. 41, No.1 (2006), 57-64.

ON COMMUTATIVITY OF σ-PRIME RINGS

L. Oukhtite and S. Salhi

Université Moulay Ismaïl, Faculté des Sciences et Techniques, Département de Mathématiques, B. P. 509-Boutalamine, Errachidia, Maroc
e-mail: oukhtite@math.net

Université Sidi Mohamed Ben Abdellah, Faculté des Sciences, Département de Mathématiques et Informatique, B. P. 1796-Atlas, Fes, Maroc
e-mail: salhi@math.net

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 subset 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.

2000 Mathematics Subject Classification.   16W10, 16W25, 16W20, 16U80.

Key words and phrases.   Rings with involution, σ-prime rings, centralizing automorphisms, square closed Lie ideals, derivations, commutativity.

Full text (PDF) (free access)

DOI: 10.3336/gm.41.1.05

References:

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