环与其商环的若干类理想

Relations Between Several Ideals of a Ring and Its Quotient Ring

本文讨论一个环R与其商环R/I之间关于若干类理想的关系.设I■K■R且K是R的理想,我们证明了K是R的二素理想(强素理想,左T-幂零理想,根对称理想)当且仅当K/I是商环R/I的二素理想(强素理想,左T-幂零理想,根对称理想).

In this note, we investigate the relationships between ideals of a ringR and its quotient ringR/I. We show that if I K R and IΔR, then K is a 2- primal ideal （ strongly prime ideal, left T- nilpotent ideal, radically-symmetric ideal ） of R if and only if K/I is a 2-primal ideal （ strongly prime ideal, left T-nilpotent ideal, radically- symmetric ideal ） of R/I.