Prime bases of weakly prime submodules and the weak radical of submodules (Q5891364)

Motivated by the background and the standard prime basis of a submodule, the paper provides some formulas on the weak radical of submodules of a module. Also, it gives a result which investigates the existence and the uniqueness of the prime basis of a weakly prime submodule. It shows that the standard prime basis of a weakly prime submodule may have distinct prime bases. After, the authors investigate when weakly prime submodules have finite standard prime bases.NEWLINENEWLINE The authors conclude the paper by giving an application to Noetherian rings, they show that:NEWLINENEWLINE If \(R\) is a Noetherian ring, then \(R\) weakly satisfies the radical formula if and only if every finally generated \(\frac{R}{N(R)}-\) module weakly satisfies the radical formula.