Some Generalizations of Q-Principally Injective Modules

Abstract

The purpose of this work is to investigate some more property of Q-finitely injective modules and generalize this idea to Q-small finitely injective modules. A quasi-f-injective module Q is non co-Hopfian if and only if there is a decomposition Q = Nr ⊕ (⊕ri=1M i) for any positive integer r, where Nr ∼=QandMi ≠ 0 for 1 ≤ i ≤ r. Also, we prove that a semi-regular module Q, an R-module P is Q-sf-injective if and only if P is Q-f-injective. © Palestine Polytechnic University-PPU 2023.