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arXiv · 1705.09224

Counting submodules of a module over a noetherian commutative ring

Yves Cornulier
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Abstract

We count the number of submodules of an arbitrary module over a countable noetherian commutative ring. We give, along the way, a structural description of meager modules, which are defined as those that do not have the square of a simple module as subquotient. We deduce in particular a characterization of uniserial modules over commutative noetherian rings.

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Yves Cornulier. 2019-06-20. Counting submodules of a module over a noetherian commutative ring. https://doi.org/10.1016/j.jalgebra.2019.06.010

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