NOTES ON THE COMMUTATIVITY OF PRIME NEAR-RINGS


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Koc E.

MISKOLC MATHEMATICAL NOTES, cilt.12, ss.193-200, 2011 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 12 Konu: 2
  • Basım Tarihi: 2011
  • Doi Numarası: 10.18514/mmn.2011.316
  • Dergi Adı: MISKOLC MATHEMATICAL NOTES
  • Sayfa Sayıları: ss.193-200

Özet

Let N be a 3-prime right near-ring and let f be a generalized (theta, theta) - derivation on N with associated. (theta, theta) - derivation d: It is proved that N must be a commutative ring if d not equal 0 and one of the following conditions is satisfied for all x; y 2 N W. i / f. O x; y _ / D 0I. i i / f([x, y]) = theta([x, y]); (iii)f (x circle y) = 0 (i) f(xoy) = theta(x circle y); (v) f([x, y]) = theta(xoy); (vi) f(xoy) = theta([x, y]). We also prove theorems which assert that N is commutative, but not necessarily a ring.