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http://dx.doi.org/10.7858/eamj.2017.008

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)

Publication Information

East Asian mathematical journal / v.33, no.1, 2017 , pp. 75-81 More about this Journal

Abstract

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.

Keywords

Reduced rings and modules; Regular and strongly regular rings;

Citations & Related Records

Reference

1	G.Azumaya, Strongly ${\pi}$ -regular Rings, Journal of Fac.Sci.Hokkaido Univ. Ser. I. 13, (1954), 34-39. MR 16, 788 DOI
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 DOI