A Note On E-Injective Modules

Abstract

Let 𝑅 be a commutative ring with identity, 𝑀 an 𝑅-module and 𝐸 a torsion-free 𝑅-module. A submodule 𝑁 of 𝑀 is said to be essential (large) in 𝑀 if the intersection of 𝑁 with each nonzero submodule of 𝑀 is nonzero, that is, 𝑁 ∩ 𝑅𝑚 ≠ 0 for any nonzero element 𝑚 ∈ 𝑀 and we write 𝑁 ≤𝑒 𝑀. It is clear that the class of 𝑒 − 𝑒𝑥𝑎𝑐𝑡 sequences is larger than the class of 𝑒𝑥𝑎𝑐𝑡 sequences. In this study we present the concept of e-injective modules as a generalization of injective modules. The main goal is to give a characterization of e-injective modules in terms of contravariant functor 𝐻𝑜𝑚(−,𝐸)