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On Semigroup Ideals of Prime Near-Rings with Semiderivation

Yıl 2017, Cilt: 7 Sayı: 2, 109 - 120, 04.01.2018

Öz

The notion of semiderivations of a ring was introduced by J.
Bergen in [5]. Considerable work has been done on commutativity of prime
near-rings with derivations in [2], [3] and [4]. In the present paper, it is
shown that is a nonzero semigroup
ideal of prime near-ring, is a nonzero
semiderivation associated with an additive mapping of such that then is commutative ring.
Also, we extend some well known results concerning semiderivations of prime
rings for a semigroup ideal of prime near-rings.

Kaynakça

  • Ashraf, M. and Boua, A., On semiderivations in prime near-rings, Commun. Korean Math. Soc., 31(3), 433-445, 2016.
  • Bell, H. E. and Mason G., On derivations in near-rings, Near-rings and Near-fields, North-Holland Mathematical Studies, 137, 31-35, 1987.
  • Bell, H. E. and Mason, G., On derivations in near-rings and rings, Math. J. Okayama Univ., 34, 135-144, 1992.
  • Bell, H. E., On derivations in near-rings II, Kluwer Academic Publishers Netherlands, 191-197, 1997.
  • Bergen, J., Derivations in prime rings, Canad. Math. Bull., 26, 267-270, 1983.
  • Boua, A. and Oukhtite, L., Semiderivations satisfying certain algebraic identities on prime near-rings, Asian-Eur. J. Math., 6(3), 1350043 (8 pp.), 2013.
  • Boua, A., Oukhtite, L. and Raji, A., Semigruop ideals with semiderivations in prime near-rings, Palestine J. Math., 3(Spec 1), 438-444, 2014.
  • Filippis, De V., Mamouni, A. and Oukhtite, L., Semiderivations satisfying certain algebraic identities on Jordan Ideals, ISRN Algebra, Article ID 738368 (7 pp.), 2013.
  • Huang, S., Semiderivations with power values on Lie ideals in prime rings, Ukranian Math. J., 65(6), 967-971, 2013.
  • Chang, J. C., On semiderivations of prime rings, Chinese J. Math., 12, 255-262, 1984.
  • Pilz, G., Near-rings, 2nd Ed. North Holland, Amsterdam, 1983.

Yarıtürevli Asal Yakın Halkaların Yarıgrup İdealleri Üzerine

Yıl 2017, Cilt: 7 Sayı: 2, 109 - 120, 04.01.2018

Öz

[5]
te J. Bergen tarafından bir halkanın yarıtürevi tanımlanmıştır. [2], [3] ve [4]
de türevli asal yakın halkaların komütatifliği ile ilgili bazı sonuçlar elde
edilmiştir. Bu makalede,
toplamsal dönüşümü ile belirlenmiş sıfırdan
farklı bir yarıtürev olmak üzere
3-asal yakın halkasının sıfırdan farklı bir yarıgrup ideali için eğer ise bu durumda  nin değişmeli bir
halka olduğu gösterilmiştir. Ayrıca yarıtürevli asal halkalarda bilinen bazı
sonuçlar asal yakın halkaların yarıgrup idealleri için ispatlanmıştır.

Kaynakça

  • Ashraf, M. and Boua, A., On semiderivations in prime near-rings, Commun. Korean Math. Soc., 31(3), 433-445, 2016.
  • Bell, H. E. and Mason G., On derivations in near-rings, Near-rings and Near-fields, North-Holland Mathematical Studies, 137, 31-35, 1987.
  • Bell, H. E. and Mason, G., On derivations in near-rings and rings, Math. J. Okayama Univ., 34, 135-144, 1992.
  • Bell, H. E., On derivations in near-rings II, Kluwer Academic Publishers Netherlands, 191-197, 1997.
  • Bergen, J., Derivations in prime rings, Canad. Math. Bull., 26, 267-270, 1983.
  • Boua, A. and Oukhtite, L., Semiderivations satisfying certain algebraic identities on prime near-rings, Asian-Eur. J. Math., 6(3), 1350043 (8 pp.), 2013.
  • Boua, A., Oukhtite, L. and Raji, A., Semigruop ideals with semiderivations in prime near-rings, Palestine J. Math., 3(Spec 1), 438-444, 2014.
  • Filippis, De V., Mamouni, A. and Oukhtite, L., Semiderivations satisfying certain algebraic identities on Jordan Ideals, ISRN Algebra, Article ID 738368 (7 pp.), 2013.
  • Huang, S., Semiderivations with power values on Lie ideals in prime rings, Ukranian Math. J., 65(6), 967-971, 2013.
  • Chang, J. C., On semiderivations of prime rings, Chinese J. Math., 12, 255-262, 1984.
  • Pilz, G., Near-rings, 2nd Ed. North Holland, Amsterdam, 1983.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Matematik
Yazarlar

Serhat Durucu Bu kişi benim

Öznur Gölbaşı

Yayımlanma Tarihi 4 Ocak 2018
Gönderilme Tarihi 16 Mayıs 2017
Kabul Tarihi 19 Aralık 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 7 Sayı: 2

Kaynak Göster

APA Durucu, S., & Gölbaşı, Ö. (2018). On Semigroup Ideals of Prime Near-Rings with Semiderivation. Adıyaman University Journal of Science, 7(2), 109-120.
AMA Durucu S, Gölbaşı Ö. On Semigroup Ideals of Prime Near-Rings with Semiderivation. ADYU J SCI. Ocak 2018;7(2):109-120.
Chicago Durucu, Serhat, ve Öznur Gölbaşı. “On Semigroup Ideals of Prime Near-Rings With Semiderivation”. Adıyaman University Journal of Science 7, sy. 2 (Ocak 2018): 109-20.
EndNote Durucu S, Gölbaşı Ö (01 Ocak 2018) On Semigroup Ideals of Prime Near-Rings with Semiderivation. Adıyaman University Journal of Science 7 2 109–120.
IEEE S. Durucu ve Ö. Gölbaşı, “On Semigroup Ideals of Prime Near-Rings with Semiderivation”, ADYU J SCI, c. 7, sy. 2, ss. 109–120, 2018.
ISNAD Durucu, Serhat - Gölbaşı, Öznur. “On Semigroup Ideals of Prime Near-Rings With Semiderivation”. Adıyaman University Journal of Science 7/2 (Ocak 2018), 109-120.
JAMA Durucu S, Gölbaşı Ö. On Semigroup Ideals of Prime Near-Rings with Semiderivation. ADYU J SCI. 2018;7:109–120.
MLA Durucu, Serhat ve Öznur Gölbaşı. “On Semigroup Ideals of Prime Near-Rings With Semiderivation”. Adıyaman University Journal of Science, c. 7, sy. 2, 2018, ss. 109-20.
Vancouver Durucu S, Gölbaşı Ö. On Semigroup Ideals of Prime Near-Rings with Semiderivation. ADYU J SCI. 2018;7(2):109-20.

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