Existence of derivations on near-rings

详细信息    查看全文

• 作者：Ahmed A. M. Kamal (1107)
  Khalid H. Al-Shaalan (1107)
  
• 关键词：Primary 16W25 ; 16Y30 ; near ; ring ; derivation ; inner derivation ; n ; distributive near ; ring ; 3 ; prime nearring
• 刊名：Mathematica Slovaca
• 出版年：2013
• 出版时间：June 2013
• 年：2013
• 卷：63
• 期：3
• 页码：431-448
• 全文大小：252KB
• 参考文献：1. Argac, N. -Bell, H. E. : / Some results on derivations in nearrings. In: Near-rings and Near-fields (Stellenbosch, 1997), Kluwer Acad. Publ., Dordrecht, 2001, pp. 42-6. CrossRef
  2. Beidar, K. I. -Fong, Y. -Wang, X. K. : / Posner and Herstein theorems for derivations of 3 / -prime near-rings, Comm. Algebra 24 (1996), 1581-589. CrossRef
  3. Bell, H. E. : / On derivations in near-rings II. In: Nearrings, Nearfields and K-loops (Hamburg, 1995). Math. Appl. 426, Kluwer Acad. Publ., Dordrecht, 1997, pp. 191-97. CrossRef
  4. Bell, H. E. : / On prime near-rings with generalized derivation, Int. J. Math. Math. Sci. (2008), Art. ID 490316, 5 p.
  5. Bell, H. E. -Argac, N. : / Derivations, products of derivations, and commutativity in near-rings, Algebra Colloq. 8 (2001), 399-07.
  6. Bell, H. E. -Mason, G. : / On derivations in near-rings. In: Near-rings and Near-fields (Tübingen, 1985). North-Holland Math. Stud. 137, North-Holland, Amsterdam, 1987, pp. 31-5.
  7. Bell, H. E. -Mason, G. : / On derivations in near-rings and rings, Math. J. Okayama Univ. 34 (1992), 135-44.
  8. Booth, G. L. -Groenewald, N. J. -Veldsman, S. : / A Kurosh-Amitsur prime radical for near-rings, Comm. Algebra 18 (1990), 3111-122. CrossRef
  9. Deng, Q. -Yenigul, M. S. -Argac, N. : / On commutativity of near-rings with derivations, Math. Proc. R. Ir. Acad. 98A (1998), 217-22.
  10. Cotti Ferrero, C. -Ferrero, G. : / Nearrings. Some Developments Linked to Semigroups and Groups. Adv. Math. (Dordr.) 4, Kluwer Academic Publishers, Dordrecht, 2002.
  11. Fong, Y. -Ke, W.-F. -Wang, C.-S. : / Nonexistence of derivations on transformation near-rings, Comm. Algebra 28 (2000), 1423-428. CrossRef
  12. Groenewald, N. J. : / Different prime ideals in near-rings, Comm. Algebra 19 (1991), 2667-675. CrossRef
  13. Holcombe, M. : / A hereditary radical for near-rings, Studia Sci. Math. Hungar. 17 (1982), 453-56.
  14. Hongan, M. : / On near-rings with derivation, Math. J. Okayama Univ. 32 (1990), 89-2.
  15. Hungerford, T. W. : / Algebra, Holt, Rinehart and Winston Inc., New York, 1974.
  16. Ligh, S. : / A note on matrix near rings, J. London Math. Soc. (2) 11 (1975), 383-84. CrossRef
  17. Meldrum, J. D. P. : / Near-rings and their links with groups. Res. Notes Math. 134, Pitman (Advanced Publishing Program), Boston, MA, 1985.
  18. Pilz, G. : / Near-rings. The theory and its applications. North-Holland Math. Stud. 23, North-Holland Publishing Co., Amsterdam, 1983.
  19. Veldsman, S. : / On equiprime near-rings, Comm. Algebra 20 (1992), 2569-587. CrossRef
  20. Wang, X. K. : / Derivations in prime near-rings, Proc. Amer. Math. Soc. 121 (1994), 361-66. CrossRef
  
• 作者单位：Ahmed A. M. Kamal (1107)
  Khalid H. Al-Shaalan (1107)
  
  1107. Department of Mathematics, College of Science, King Saud University, King Saud, Saudi Arabia
  

文摘

We obtain conditions on (R,+) which force that the zero map is the only derivation on a zero-symmetric near-ring R. Throughout the paper we construct several new examples of near-rings which are not rings admitting non-zero derivations, non-zero (σ, σ)-derivations and non-zero (1, σ)-derivations.