Counting submodules of a module over a noetherian commutative ring
Commutative Algebra
2019-07-03 v2
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.
Cite
@article{arxiv.1705.09224,
title = {Counting submodules of a module over a noetherian commutative ring},
author = {Yves Cornulier},
journal= {arXiv preprint arXiv:1705.09224},
year = {2019}
}
Comments
34 pages. v2: expanded introduction and preliminaries