Glasnik matematički, Vol. 41 No. 1, 2006.
Izvorni znanstveni članak
On commutativity of σ-prime rings
L. Oukhtite
S. Salhi
Sažetak
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.
Ključne riječi
Rings with involution; σ-prime rings; centralizing automorphisms; square closed Lie ideals; derivations; commutativity
Hrčak ID:
3298
URI
Datum izdavanja:
24.5.2006.
Posjeta: 1.036 *