Journals / Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics / 2005 / Cilt: 54 - Sayı: 2
Some results on near-rings with generalized derivations
- Journal
- Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
- Pages
- 21–26
- DOI
- —
Abstract
Let N be a prime right, near-ring with multiplicative center Z, f : R $rightarrow$ R a generalized derivation associated with derivation d. The following results are proved: (i) If $f^2(N) = 0$ then f = 0. (ii) If $f(N)subset Z$ then N is commutative ring. (iii) f(xy) = f(x)f(y) or f(xy) = f(y)f(x) for all x,y $in$ N then d = 0.
Özet
n merkezi Z olan bir sağ asal near-halka, f : N $rightarrow$TV tanımlı d ile ilgili bir genelleştirilmiş türev olsun. Bu durumda: (i) Eğer $f^2(N) = 0$ ise f = 0 dır. (ii) Eğer $f(N)subset Z$ ise N değişmeli bir halkadır, (iii) Eğer her x,y $in$ N için f(xy) = f(x)f(y) veya f(xy) = f(y)f(x) ise d = 0 dır.