A note on weak regularity in general rings
- 70 Downloads
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.
KeywordsWeak 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.
- 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
- 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
- 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