A Note On E-Injective Modules

Year 2022, Volume: 26 Issue: 6, 1262 - 1266, 31.12.2022

Abuzer Gündüz Osama Naji

https://doi.org/10.16984/saufenbilder.1094262

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)

Keywords

E-Injective Modules, E-Exact Sequences, Contravariant Functor

References

• [1] I. Akray, A. Zebari, “Essential exact sequences,” Communications of the Korean Mathematical Society, 2020; 35(2):469-480.
• [2] A. Tercan, C. C. Yücel, “Module Theory, Extending Modules and Generalizations,” Bassel: Birkhäuser, Springer, 2016.
• [3] J. J. Rotman, J. J. Rotman, “An introduction to homological algebra,” New York: Springer, 2009.