Small理想都是投射的环(英文)

Rings Whose Small Ideals Are Projective

若对任意真理想K,有K+I≠R,则称环R的右理想I为small理想.若任意small右理想是投射的,则称环R为右J-遗传环.引入右J-遗传环作为右遗传环的推广,给出了右J-遗传环的一些例子和性质.利用右J-遗传环得到了半本原环的一些新刻画.

A right ideal I of a ring R is small in case for every proper right ideal K of R,K + I≠ R.The ring R is called a right J-hereditary ring if every small right ideal is projective.Right J-hereditary rings is developed as a generalization of right hereditary rings.Many properties of right J-hereditary rings are obtained.Several new characterizations of semiprimitive rings in terms of right J-hereditary rings are obtained.Related examples are given as well.