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)
Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Research Articles |
Authors | |
Publication Date | December 31, 2022 |
Submission Date | March 28, 2022 |
Acceptance Date | October 22, 2022 |
Published in Issue | Year 2022 |
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