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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 45 Issue: 2

Semiprime and weakly compressible modules

N. Dehghani
M. R. Vedadi
Pages
—
Publication Date
2016-04-01
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

These considerations settle two questions, namely Qu 1, and Qu 2, in [6, p 92].

📌 3 Key Takeaways

🎯
Objective & Hypothesis:An R-module M is called semiprime (resp. weakly compressible) if it is cogenerated by each of its essential submodules (resp.
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Key Findings & Data:HomR(M, N)N is nonzero for every 0 6= N ≤ MR).
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Conclusion & Impact:These considerations settle two questions, namely Qu 1, and Qu 2, in [6, p 92].
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Krull dimension · semiprime module · singular semi-Artinian ring

Abstract

An R-module M is called semiprime (resp. weakly compressible) if it is cogenerated by each of its essential submodules (resp. HomR(M, N)N is nonzero for every 0 6= N ≤ MR). We carry out a study of weakly compressible (semiprime) modules and show that there exist semiprime modules which are not weakly compressible. Weakly compressible modules with enough critical submodules are characterized in different ways. For certain rings R, including prime hereditary Noetherian rings, it is proved that MR is weakly compressible (resp. semiprime) if and only if M ∈ Cog(Soc(M) ⊕ R) and M/Soc(M) ∈ Cog(R) (resp. M ∈ Cog(Soc(M) ⊕ R)). These considerations settle two questions, namely Qu 1, and Qu 2, in [6, p 92].

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Cite This Article

Dehghani, N., Vedadi, M. R. (2016). Semiprime and weakly compressible modules. Hacettepe Journal of Mathematics and Statistics, Volume: 45 Issue: 2. https://ajindex.com/articles/1403163

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