On ECG-extending and ECG-quasi-continuous modules

الملخص EN

It is shown that a finitely generated non-M-singular left R-module M is noetherian if and only if M has finite uniform dimension and the direct sum of every countable collection of M-injective left R-modules in σ [M] is ecg-extending.

It is also shown that an ecgquasi- continuous left R-module M has indecomposable decomposition if the union of any chain of local direct summands of M is a direct sum of countably generated submodules.