Notes on Prime Near-Rings with Multiplicative Derivation

Yıl 2017, Cilt: 38 Sayı: 2, 355 - 363, 24.04.2017

Zeliha Bedir Öznur Gölbaşı

https://doi.org/10.17776/cumuscij.290566

Cited By: 2

Öz

Let  be a left near ring. A
map   is called a nonzero
multiplicative derivation if  holds for all  In the present paper,
we shall extend some well known results concerning commutativity of prime rings
for nonzero multiplicative derivations of a left prime near-ring 

Anahtar Kelimeler

near-ring, multiplicative derivation, Prime ring, derivation, multiplicative derivation

Çarpımsal Türevli Asal Yakın Halkalar Üzerine Notlar

Öz

bir
sol yakın halka olsun.  dönüşümü her  için  koşulunu sağlıyorsa  ye bir çarpımsal türev denir. Bu makalede,
asal halkalarda iyi bilinen bazı komütatiflik koşulları, çarpımsal türevli sol
asal yakın halkalar için genelleştirilecektir.

Anahtar Kelimeler

Asal halka, yakın halka, türev, çarpımsal türev

Kaynakça

• [1]. Bell, H. and Mason, G., On derivations in near rings, Near rings and Near fields, North-Holland Mathematical Studies, 137, 31-35, (1987).
• [2]. Bell, H. E., On derivations in near-rings II, Kluwer Academic Pub. Math. Appl., Dordr., 426, 191-197, (1997).
• [3]. Bell, H. E. and Kappe, L. C., Rings in which derivations satisfy certain algebraic conditions, Acta Math. Hungarica, 53, 339-346, (1989).
• [4]. Daif, M. N., When is a multiplicative derivation additive, Int. J. Math. Math. Sci., 14(3), 615-618, (1991).
• [5]. Daif, M. N. and Bell, H. E., Remarks on derivations on semiprime rings, Int. J. Math. Math. Sci., 15(1), 205-206, (1992).
• [6]. Goldman, H. and Semrl, P., Multiplicative derivations on , Monatsh Math., 121(3), 189-197, (1969).
• [7]. Herstein, I. N., A note on derivations, Canad. Math. Bull., 21(3), 369-370, (1978).
• [8]. Martindale III, W. S., When are multiplicative maps additive, Proc. Amer. Math. Soc., 21, 695-698, (1969).
• [9]. Kamal, A. M. and Al-Shaalan, K. H., Existence of derivations on near-rings, Math. Slovaca, 63, no:3, 431-438, (2013).
• [10]. Koç, E. and Gölbaşı, Ö., Semiprime near-rings with multiplicative generalized derivations, Fasciculi Mathematici, 57, 105-119, (2016).
• [11]. Posner, E. C. Derivations in Prime Rings, Proc. Amer. Math. Soc., 8, 1093-1100, (1957).