湖南师范大学自然科学学报
湖南師範大學自然科學學報
호남사범대학자연과학학보
ACTA SCIENTIARUM NATURALIUM UNIVERSITATIS NORMALIS HUNANENSIS
2012年
1期
1-4
,共4页
J-遗传环%small内射模%覆盖
J-遺傳環%small內射模%覆蓋
J-유전배%small내사모%복개
J-hereditary rings%small injective modules%covers
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.
若對任意真理想K,有K+I≠R,則稱環R的右理想I為small理想.若任意small右理想是投射的,則稱環R為右J-遺傳環.引入右J-遺傳環作為右遺傳環的推廣,給齣瞭右J-遺傳環的一些例子和性質.利用右J-遺傳環得到瞭半本原環的一些新刻畫.
약대임의진이상K,유K+I≠R,칙칭배R적우이상I위small이상.약임의small우이상시투사적,칙칭배R위우J-유전배.인입우J-유전배작위우유전배적추엄,급출료우J-유전배적일사례자화성질.이용우J-유전배득도료반본원배적일사신각화.
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.
