Çarpımsal Türevli Asal Yakın Halkalar Üzerine Notlar

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

Notes on Prime Near-Rings with Multiplicative Derivation

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

Keywords:

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

PDF

___

[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).