Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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TOPOLOGICAL CONDITIONS OF NI NEAR-RINGS

  • Dheena, P. (Department of Mathematics Annamalai University) ;
  • Jenila, C. (Department of Mathematics Annamalai University)
  • Received : 2011.12.23
  • Published : 2013.10.31
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Abstract

In this paper we introduce the notion of NI near-rings similar to the notion introduced in rings. We give topological properties of collection of strongly prime ideals in NI near-rings. We have shown that if N is a NI and weakly pm near-ring, then $Max(N)$ is a compact Hausdorff space. We have also shown that if N is a NI near-ring, then for every $a{\in}N$, $cl(D(a))=V(N^*(N)_a)=Supp(a)=SSpec(N){\setminus}int\;V(a)$.

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References

  1. G. F. Birkenmeier, J. Y. Kim, and J. K. Park, Regularity conditions and the simplicity of prime factor rings, J. Pure Appl. Algebra 115 (1997), no. 3, 213-230. https://doi.org/10.1016/S0022-4049(96)00011-4
  2. P. Dheena and D. Sivakumar, On strongly 0-prime ideals in near-rings, Bull. Malays. Math. Sci. Soc. (2) 27 (2004), no. 1, 77-85.
  3. S. U. Hwang, Y. C. Jeon, and Y. Lee, Structure and topological conditions of NI rings, J. Algebra 302 (2006), no. 1, 186-199. https://doi.org/10.1016/j.jalgebra.2006.02.032
  4. J. Lambek, On the representations of modules by sheaves of factor modules, Canad. Math. Bull. 14 (1971), 359-368. https://doi.org/10.4153/CMB-1971-065-1
  5. G. Marks, On 2-primal Ore extensions, Comm. Algebra 29 (2001), no. 5, 2113-2123. https://doi.org/10.1081/AGB-100002173
  6. G. Marks, A taxonomy of 2-primal rings, J. Algebra 266 (2003), no. 2, 494-520. https://doi.org/10.1016/S0021-8693(03)00301-6
  7. J. R. Munkres, Topology, Prentice-Hall of India, New Delhi, 2005.
  8. G. Pilz, Near-Rings, North-Holland, Amsterdam, 1983.
  9. K. Samei, The zero-divisor graph of a reduced ring, J. Pure Appl. Algebra 209 (2007), no. 3, 813-821. https://doi.org/10.1016/j.jpaa.2006.08.008
  10. S. H. Sun, Noncommutative rings in which every prime ideal is contained in a unique maximal ideal, J. Pure Appl. Algebra 76 (1991), no. 2, 179-192. https://doi.org/10.1016/0022-4049(91)90060-F