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

Semiprime and weakly compressible modules

N. Dehghani
M. R. Vedadi
Sayfa
—
Yayın Tarihi
2016-04-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri:HomR(M, N)N is nonzero for every 0 6= N ≤ MR).
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Sonuç & Katkı:These considerations settle two questions, namely Qu 1, and Qu 2, in [6, p 92].
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (12)

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