Amply essential g-supplemented modules

İngilizce (OpenAlex)

Let M be an R-module.If every essential submodule of M has a g-supplement in M, then M is called an essential g-supplemented (or briefly, eg-supplemented) module.If every essential submodule has ample g-supplements in M, then M is called an amply essential gsupplemented (or briefly, amply eg-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 amply eg-supplemented module are amply eg-supplemented.Let M be a projective and eg-supplemented module.Then every finitely Mgenerated R-module is amply egsupplemented.