Semiprime and weakly compressible modules
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].
Keywords:
Krull dimension, semiprime module singular semi-Artinian ring, weakly compressible module,
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- Yayın Aralığı: Yılda 6 Sayı
- Başlangıç: 2002
- Yayıncı: Hacettepe Üniversitesi Fen Fakultesi