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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
The main goal is to give a characterization of e-injective modules in terms of contravariant functor 𝐻𝑜𝑚(−,𝐸)
📌 3 Key Takeaways
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Objective & Hypothesis:Let 𝑅 be a commutative ring with identity, 𝑀 an 𝑅-module and 𝐸 a torsion-free 𝑅-module.
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Key Findings & Data: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.
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Conclusion & Impact:The main goal is to give a characterization of e-injective modules in terms of contravariant functor 𝐻𝑜𝑚(−,𝐸)
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:E-Injective Modules · E-Exact Sequences · Contravariant Functor
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)
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Cite This Article
Gündüz, A., Naji, O. (2022). A Note On E-Injective Modules. Sakarya University Journal of Science, Volume: 26 Issue: 6. https://doi.org/10.16984/saufenbilder.1094262