Study on AGP-injective rings satisfying certain finite conditions
LU Qi
CHEN Huaxi
WEI Wenlian
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.
Keywords：semisimple ringAGP-injective ringnonsingular ringGW-ideal
Publication Date：2025-11-30
Online Publishing Date：2025-12-12(First online date of this platform, not the publication date of the document)
Pages：4( 52-55 )