具有奇异单模是YJ-内射的环与正则环

RINGS WHOSE SIMPLE SINGULAR MODULES ARE YJ-INJECTIVE AND REGULAR RINGS

主要证明了 :如果R是右拟 -duo环 ,且每一个单奇异右R -模M是YJ-内射的 ,那么 :(1)如果N1(R)是正则的 ,则R是正则的 ;(2 )如果N0 (R)是正则的 ,则R是正则的 ;(3)如果R是正规环 ,则R是正则的 ;(4)如果N0 (R) C(R) 。

This paper proves mainly that if is R a right qusi-duo ring whose every singular simple right R-module M is YJ-injective, then (1)if N 1(R) is regular, then R is regular; (2)if N 0(R) is regular, then R is regular; (3)if R is abelian, then R is regular; (4)if N 0(R)C(R),then R is regular.