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On minimal prime submodules. (English) Zbl 1041.16002

Summary: It is shown that if every prime left ideal minimal over an ideal \(I\) is finitely generated, then there are only finitely many prime left ideals minimal over \(I\). This immediately generalizes Cohen’s theorem. We also extend the former result to multiplication modules over commutative rings.

MSC:

16D80 Other classes of modules and ideals in associative algebras
16P40 Noetherian rings and modules (associative rings and algebras)
16D25 Ideals in associative algebras
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