Abstract
Let M and N be two modules. M is called essentially pseudo N-injective if for any essential submodule A of N, any monomorphism \(f : A \rightarrow M\) can be extended to some \(g \in Hom(N, M)\). M is called essentially pseudo-injective if M is essentially pseudo M-injective. Basic properties of mutually essentially pseudo-injective modules and essentially pseudo-injective modules are proved and their connections with pseudo-injective modules are addressed.
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