| Abstract: | Let X be a left R-module. We characterize when the direct sum of two X-extending modules is X-extending via essential injectivity and pseudo injectivity of modules. As a corollary, we show that if extending modules M 1 and M 2 are relatively essentially injective and M 1 is pseudo-M 2-injective (or M 2 is pseudo-M 1-injective) then M 1 ⊕ M 2 is extending. Also we characterize when the direct sum of two CESS-modules is CESS. Some characterizations of almost Noetherian rings are also given by relative (quasi-) continuity of left R-modules. |
