Indecomposable integrally closed modules of arbitrary rank over a two-dimensional regular local ring
Commutative Algebra
2021-12-07 v1
Abstract
In this paper, we construct indecomposable integrally closed modules of arbitrary rank over a two-dimensional regular local ring. The modules are quite explicitly constructed from a given complete monomial ideal. We also give structural and numerical results on integrally closed modules. These are used in the proof of indecomposability of the modules. As a consequence, we have a large class of indecomposable integrally closed modules of arbitrary rank whose ideal is not necessarily simple. This extends the original result on the existence of indecomposable integrally closed modules and strengthens the non-triviality of the theory developed by Kodiyalam.
Cite
@article{arxiv.2112.02885,
title = {Indecomposable integrally closed modules of arbitrary rank over a two-dimensional regular local ring},
author = {Futoshi Hayasaka},
journal= {arXiv preprint arXiv:2112.02885},
year = {2021}
}
Comments
24 pages, 1 figure. arXiv admin note: text overlap with arXiv:1809.07944