On the nilpotence of the prime radical in module categories

• Veröffentlicht in: Algebra and Discrete Mathematics
• Datum: 2021
• Hauptverfasser: Arellano, C., Castro, J., Ríos, J.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут прикладної математики і механіки НАН України 2021
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/188745
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: On the nilpotence of the prime radical in module categories / C. Arellano, J. Castro, J. Ríos // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 2. — С. 161-184. — Бібліогр.: 18 назв. — англ.

For M ∈ R-Mod and τ a hereditary torsion theory on the category σ[M] we use the concept of prime and semiprime module defined by Raggi et al. to introduce the concept of τ-pure prime radical Nτ (M) = Nτ as the intersection of all τ-pure prime submodules of M. We give necessary and sufficient conditi...