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Notes on Prime Near-Rings with Multiplicative Derivation

Year 2017, Volume: 38 Issue: 2, 355 - 363, 24.04.2017
https://doi.org/10.17776/cumuscij.290566

Abstract

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 

References

  • [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).

Çarpımsal Türevli Asal Yakın Halkalar Üzerine Notlar

Year 2017, Volume: 38 Issue: 2, 355 - 363, 24.04.2017
https://doi.org/10.17776/cumuscij.290566

Abstract

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.

References

  • [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).
There are 11 citations in total.

Details

Subjects Engineering
Journal Section Special
Authors

Zeliha Bedir

Öznur Gölbaşı

Publication Date April 24, 2017
Published in Issue Year 2017 Volume: 38 Issue: 2

Cite

APA Bedir, Z., & Gölbaşı, Ö. (2017). Notes on Prime Near-Rings with Multiplicative Derivation. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, 38(2), 355-363. https://doi.org/10.17776/cumuscij.290566
AMA Bedir Z, Gölbaşı Ö. Notes on Prime Near-Rings with Multiplicative Derivation. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. April 2017;38(2):355-363. doi:10.17776/cumuscij.290566
Chicago Bedir, Zeliha, and Öznur Gölbaşı. “Notes on Prime Near-Rings With Multiplicative Derivation”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 38, no. 2 (April 2017): 355-63. https://doi.org/10.17776/cumuscij.290566.
EndNote Bedir Z, Gölbaşı Ö (April 1, 2017) Notes on Prime Near-Rings with Multiplicative Derivation. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 38 2 355–363.
IEEE Z. Bedir and Ö. Gölbaşı, “Notes on Prime Near-Rings with Multiplicative Derivation”, Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 38, no. 2, pp. 355–363, 2017, doi: 10.17776/cumuscij.290566.
ISNAD Bedir, Zeliha - Gölbaşı, Öznur. “Notes on Prime Near-Rings With Multiplicative Derivation”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 38/2 (April 2017), 355-363. https://doi.org/10.17776/cumuscij.290566.
JAMA Bedir Z, Gölbaşı Ö. Notes on Prime Near-Rings with Multiplicative Derivation. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2017;38:355–363.
MLA Bedir, Zeliha and Öznur Gölbaşı. “Notes on Prime Near-Rings With Multiplicative Derivation”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 38, no. 2, 2017, pp. 355-63, doi:10.17776/cumuscij.290566.
Vancouver Bedir Z, Gölbaşı Ö. Notes on Prime Near-Rings with Multiplicative Derivation. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2017;38(2):355-63.