Journals / Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics / 2019 / Cilt: 68 - Sayı: 1
ON COMMUTATIVITY OF PRIME NEAR-RINGS WITH MULTIPLICATIVE GENERALIZED DERIVATION
- Journal
- Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
- Pages
- 209–221
- DOI
- —
Abstract
In the present paper, we shall prove that 3prime near-ring Nis commutative ring, if any one of the following conditions are satisÖed: (i)f(N) Z; (ii) f([x; y]) = 0; (iii) f([x; y]) = [x; y]; (iv) f([x; y]) = (xoy);(v) f([x; y]) = [f(x); y]; (vi) f([x; y]) = [x; f(y)]; (vii) f([x; y]) = [d(x); y]; (viii)f([x; y]) = d(x)oy;(ix) [f(x); y] 2 Z for all x; y 2 N where f is a nonzero multiplicative generalized derivation of N associated with a multiplicative derivationd: