Essential radical supplemented modules

[摘要] In this work, (amply) essential radical supplemented modules are defined and some properties of these modules are investigated. Let M be an R-module and M = M1 + M2 +···+ Mn. If Mi is essential radical supplemented for every i = 1,2,...,n, then M is also essential radical supplemented. It is proved that every factor module and every homomorphic image of an essential radical supplemented module are essential radical supplemented. Let M be an essential radical supplemented R-module. Then every finitely M-generated R-module is essential radical supplemented.

[学科分类] 数学（综合）

[关键词] small submodules;essential submodules;radical;generalized (radical) supplemented modules