A note on weak regularity in general rings

  • D. I. C. Mendes
Original Paper


We investigate weak regularity in general rings. Some well known results on left weakly regular rings with identity are extended to left weakly regular rings which do not necessarily have identity.


Weak regularity Prime ideal Strongly prime ideal  2-Primal ring Reduced ring 

Mathematics Subject Classification (2000)

Primary 16E50 Secondary 16N60 16N20 



The author would like to thank the referee for his valuable suggestions and remarks which helped to improve this paper. This research was supported by FEDER and Portuguese funds through the Centre for Mathematics (University of Beira Interior) and the Portuguese Foundation for Science and Technology (FCT- Fundação para a Ciência e a Tecnologia), Project PEst-OE/MAT/UI0212/2012.


  1. Birkenmeier, G.F., Kim, J.Y., Park, J.K.: A connection between weak regularity and the simplicity of prime factor rings. Proc. Am. Math. Soc. 122(1), 53–58 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  2. Birkenmeier, G.F., Kim, J.Y., Park, J.K.: Regularity conditions and the simplicity of prime factor rings. J. Pure Appl. Algebra 115, 213–230 (1997)Google Scholar
  3. Divinsky, N.J.: Rings and Radicals. Univ. of Toronto Press, Toronto (1965)zbMATHGoogle Scholar
  4. Fisher, J.W., Snider, R.L.: On the von Neumann regularity of rings with regular prime factor rings. Pac. J. Math. 54(1), 135–144 (1974)Google Scholar
  5. Heatherly, H.E., Tucci, R.P.: Right weakly regular rings: a survey. Ring and Module Theory (Trends in Mathematics), pp. 115–123 (2010)Google Scholar
  6. Hong, C.Y., Jeon, Y.C., Kim, K.H., Kim, N.K., Lee, Y.: Weakly regular rings with ACC on annihilators and maximality of strongly prime ideals of weakly regular rings. J. Pure Appl. Algebra 207, 565–574 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  7. Hong, C.Y., Kim, N.K., Kwak, T.K.: On rings whose prime ideals are maximal. Bull. Korean Math. Soc. 37, 1–9 (2000)MathSciNetzbMATHGoogle Scholar
  8. Ramamurthi, V.S.: Weakly regular rings. Can. Math. Bull. 16(3), 317–321 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  9. Shin, G.: Prime ideals and sheaf representation of a pseudo symmetric ring. Trans. Am. Math. Soc. 184, 43–60 (1973)CrossRefGoogle Scholar
  10. Tuganbaev, A.: Rings Close to Regular. Kluwer Academic Publishers, Boston (2002)CrossRefzbMATHGoogle Scholar

Copyright information

© The Managing Editors 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Beira InteriorCovilhaPortugal

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