环与其商环的若干类理想

数学理论与应用 ›› 2016, Vol. 36 ›› Issue (3): 5-11.

环与其商环的若干类理想

管正雄, 王尧

南京信息工程大学数学与统计学院,南京,210044

出版日期:2016-09-30 发布日期:2020-09-27
基金资助:
江苏省自然科学基金(BK20141476)

Relations Between Several Ideals of a Ring and Its Quotient Ring

Guan Zhengxiong, Wang Yao

School of Mathematics and Statistics,Nanjing University of information Science and Technology,Nanjing 210044,China

Online:2016-09-30 Published:2020-09-27

摘要/Abstract

摘要： 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).

关键词: 商环, 二素理想, 强素理想, 左T, -幂零理想, 根对称理想

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

管正雄, 王尧.

环与其商环的若干类理想 [J]. 数学理论与应用, 2016, 36(3): 5-11.

Guan Zhengxiong, Wang Yao.

Relations Between Several Ideals of a Ring and Its Quotient Ring [J]. Mathematical Theory and Applications, 2016, 36(3): 5-11.