Abstract: In this note,we investigate the relationships between ideals of a ring Rand its quotient ring R/I.We show that if I ⊆K ⊆ Rand I△R,then Kis a 2-primal ideal(strongly prime ideal,left T-nilpotent ideal, radically-symmetric ideal)of Rif and only if K/Iis a 2-primal ideal(strongly prime ideal,left T-nilpotent ideal,radically-symmetric ideal)of R/I.

Key words: Quotient ring, 2-primal ideal, Strongly prime ideal, Left T-nilpotent ideal, Radically-symmetric ideal