Equivalence of Almost N‐Automorphism‐Invariant and Almost N‐Pseudo‐Injective Modules

The objective of this work is to generalize a result of Fuchigami, Kuratomi, and Shibata, published in the Journal of Algebra and Its Applications, Vol. 23, No. 2, 2450027(2024). According to this result, almost N‐invariant modules and almost N‐injective modules are equivalent. This equivalence was established by examining the homomorphisms between their injective hulls and considering certain conditions. Furthermore, they investigated the relationship between generalized N‐injective, almost N‐injective, and N‐almost‐invariant modules. Extending this work, we introduce a new generalization of these modules, which we call almost N‐automorphism‐invariant modules. We examine their characteristics and injective hulls under specific isomorphism conditions. We also investigate their equivalence to almost N‐pseudo‐injective modules in the context of module extensions.