East Asian mathematical journal

  • 제33권1호
  • /
  • Pages.75-81
  • /
  • 2017
  • /
  • 1226-6973(pISSN)
  • /
  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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REDUCED MODULES AND STRONGLY REGULAR RINGS

  • Huh, Chan (Department of Mathematics Pusan National University) ;
  • Cheon, Jeoung Soo (Department of Mathematics Pusan National University) ;
  • Kim, Du Won (Department of Mathematics Pusan National University)
  • 투고 : 2016.11.07
  • 심사 : 2017.01.20
  • 발행 : 2017.01.31
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초록

It is a well-known fact that a ring R is regular if and only if every left R-modules is flat. In this article we prove that a ring R is strongly regular if and only if every left R-modules is reduced if and only if every left-R modules is quasi-reduced.

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참고문헌

  1. G.Azumaya, Strongly ${\pi}$-regular Rings, Journal of Fac.Sci.Hokkaido Univ. Ser. I. 13, (1954), 34-39. MR 16, 788 https://doi.org/10.14492/hokmj/1530842562
  2. A.Buhpang and M.Rege, Semicommutative modules and Armendariz modules, Arab Journal of Math. Sci.18(2002), 53-65
  3. K.R.Goordearl, Von Neumann Regular Rings, Pitman Publ, (1979)
  4. J.Lambek, Lectures on rings and modules, Blaisdell Publishing Company (1966)
  5. C.P.Zhang and J.L.Chen, ${\alpha}$-Skew Armendariz and ${\alpha}$-Semicommutative modules, Taiwan.J. Of Math. Vol. 12, No. 2, (2008), 473-486 https://doi.org/10.11650/twjm/1500574168