佛山科学技术学院学报（自然科学版）2025，Vol.43Issue(6)：52-55,4.
基于有限条件的AGP-内射环研究
Study on AGP-injective rings satisfying certain finite conditions
摘要
Abstract
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 left-modules 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.关键词
半单环/AGP-内射环/非奇异环/GW-理想Key words
semisimple ring/AGP-injective ring/nonsingular ring/GW-ideal分类
数理科学引用本文复制引用
鲁琦,陈华喜,韦文联..基于有限条件的AGP-内射环研究[J].佛山科学技术学院学报（自然科学版）,2025,43(6):52-55,4.基金项目
安徽省高等学校省级质量工程项目(2023ylyjh056,2023ylyjh055,2023jyxm0826,2024aijy416) （2023ylyjh056,2023ylyjh055,2023jyxm0826,2024aijy416）
蚌埠学院质量工程重点项目(2024jyxm3,2024jyxm4) （2024jyxm3,2024jyxm4）
