Essential g-radical supplemented modules

[摘要] Let M be an R-module. If every essential submodule of M has a g-radical supplement in M, then M is called an essential g-radical supplemented (or briefly eg-radical supplemented) module. In this work, some properties of these modules are investigated. It is proved that every factor module and every homomorphic image of an eg-radical supplemented module are eg-radical supplemented. Let M be an eg-radical supplemented module. Then every finitely M-generated R-module is eg-radical supplemented.

[学科分类] 数学（综合）

[关键词] essential submodules;g-small submodules;generalized radical;g-supplemented modules