대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제36권1호
  • /
  • Pages.27-39
  • /
  • 2021
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ANNIHILATING PROPERTY OF ZERO-DIVISORS

  • Jung, Da Woon (Finance.Fishery.Manufacture Industrial Mathematics Center on Big Data Pusan National University) ;
  • Lee, Chang Ik (Department of Mathematics Pusan National University) ;
  • Lee, Yang (Department of Mathematics Pusan National University) ;
  • Nam, Sang Bok (Department of Computer Engineering Kyungdong University) ;
  • Ryu, Sung Ju (Department of Mathematics Pusan National University) ;
  • Sung, Hyo Jin (Department of Mathematics Pusan National University) ;
  • Yun, Sang Jo (Department of Mathematics Dong-A University)
  • 투고 : 2020.05.25
  • 심사 : 2020.11.02
  • 발행 : 2021.01.31
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초록

We discuss the condition that every nonzero right annihilator of an element contains a nonzero ideal, as a generalization of the insertion-of-factors-property. A ring with such condition is called right AP. We prove that a ring R is right AP if and only if Dn(R) is right AP for every n ≥ 2, where Dn(R) is the ring of n by n upper triangular matrices over R whose diagonals are equal. Properties of right AP rings are investigated in relation to nilradicals, prime factor rings and minimal order.

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참고문헌

  1. H. E. Bell, Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc. 2 (1970), 363-368. https://doi.org/10.1017/S0004972700042052
  2. J. L. Dorroh, Concerning adjunctions to algebras, Bull. Amer. Math. Soc. 38 (1932), no. 2, 85-88. https://doi.org/10.1090/S0002-9904-1932-05333-2
  3. K. E. Eldridge, Orders for finite noncommutative rings with unity, Amer. Math. Monthly 73 (1966), 376-377. https://doi.org/10.2307/2315402
  4. K. R. Goodearl and R. B. Warfield, Jr., An introduction to noncommutative Noetherian rings, London Mathematical Society Student Texts, 16, Cambridge University Press, Cambridge, 1989.
  5. Y. Hirano, D. van Huynh, and J. K. Park, On rings whose prime radical contains all nilpotent elements of index two, Arch. Math. (Basel) 66 (1996), no. 5, 360-365. https://doi.org/10.1007/BF01781553
  6. C. Huh, Y. Lee, and A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra 30 (2002), no. 2, 751-761. https://doi.org/10.1081/AGB-120013179
  7. 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
  8. S. U. Hwang, N. K. Kim, and Y. Lee, On rings whose right annihilators are bounded, Glasg. Math. J. 51 (2009), no. 3, 539-559. https://doi.org/10.1017/S0017089509005163
  9. N. Jacobson, Some remarks on one-sided inverses, Proc. Amer. Math. Soc. 1 (1950), 352-355. https://doi.org/10.2307/2032383
  10. Y. C. Jeon, H. K. Kim, Y. Lee, and J. S. Yoon, On weak Armendariz rings, Bull. Korean Math. Soc. 46 (2009), no. 1, 135-146. https://doi.org/10.4134/BKMS.2009.46.1.135
  11. N. K. Kim and Y. Lee, Extensions of reversible rings, J. Pure Appl. Algebra 185 (2003), no. 1-3, 207-223. https://doi.org/10.1016/S0022-4049(03)00109-9
  12. P. P. Nielsen, Semi-commutativity and the McCoy condition, J. Algebra 298 (2006), no. 1, 134-141. https://doi.org/10.1016/j.jalgebra.2005.10.008