MMN-4568
Rings characterized by the extending property for finitely generated submodules
Banh Duc Dung;
Abstract
A module M is called ef-extending if every closed submodule which contains essentially a finitely generated submodule is a direct summand of M. In this paper, we prove some properties of rings via ef-extending modules and essentially finite injective modules. It is shown that a module M is an ef-extending module and whenever M = H ⊕ K with H essentially finite, then H is essentially finite K-injective if and only if for essentially finite submodules N1,N2 of M with N1 ∩ N2 = 0, there exist submodules M1,M2 of M such that Ni is essential in Mi (i = 1,2) and M1 ⊕ M2 is a direct summand of M. A ring R is right co-Harada if and only if R is right (or left) perfect with ACC on right annihilators and R ⊕ R is ef-extending as a right R-module, iff R is right (or left) perfect and RR(ℕ ) is an ef-extending module. Some properties of ef-extending modules over excellent extension rings are considered.
Vol. 25 (2024), No. 2, pp. 659-672