A generalization of supplemented modules

Yongduo Wang
2016 Hacettepe Journal of Mathematics and Statistics  
Let M be a left module over a ring R and I an ideal of R. M is called an I-supplemented module (finitely I-supplemented module) if for every submodule (finitely generated submodule ) This definition generalizes supplemented modules and δ-supplemented modules. We characterize I-semiregular, I-semiperfect and I-perfect rings which are defined by Yousif and Zhou [12] using I-supplemented modules. Some well known results are obtained as corollaries.
doi:10.15672/hjms.20164512487 fatcat:z6lufhabh5gdpnb7twoxdnyroq