摘要
对GP-内射环的一些结论进行推广,研究了满足零化子升链有限条件的AGP-内射环,证明了不包含无限多个非零主左理想直和的左非奇异左AGP-内射环是半单环。用GW-理想替换理想,证明了若任意单奇异左R-模是AGP-内射的,且R的极大本质左理想是GW-理想,则R是左非奇异环。丰富了AGP-内射环的相关结果。
This study generalizes some conclusions on GP-injective rings and investigates AGP-injective rings satisfying finiteness conditions on the ascending chain of annihilators.It is proved that left nonsingular left AGP-injective rings that do not contain an infinite direct sum of non-zero principal left ideals are semisimple rings.By replacing ideals with GW-ideals,it is further proved that if every simple singular leftmodules are AGP-injective,and any maximal essential left ideal of are GW-ideal,then R is left nonsingular.These results further enrich the theory of AGP-injective rings.
作者
鲁琦
陈华喜
韦文联
LU Qi;CHEN Huaxi;WEI Wenlian(School of Mathematics and Physics,Bengbu University,Bengbu 233030,China)
基金
安徽省高等学校省级质量工程项目(2023ylyjh056,2023ylyjh055,2023jyxm0826,2024aijy416)
蚌埠学院质量工程重点项目(2024jyxm3,2024jyxm4)
