TY - JOUR
T1 - Indecomposable integrally closed modules of arbitrary rank over a two-dimensional regular local ring
AU - Hayasaka, Futoshi
N1 - Funding Information:
I would like to thank the referee for his/her careful reading and comments. This work was supported by JSPS KAKENHI Grant Number JP20K03535 .
Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2022/8
Y1 - 2022/8
N2 - 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.
AB - 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.
KW - Indecomposable module
KW - Integral closure
KW - Monomial ideal
KW - Regular local ring
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U2 - 10.1016/j.jpaa.2022.107026
DO - 10.1016/j.jpaa.2022.107026
M3 - Article
AN - SCOPUS:85123643980
SN - 0022-4049
VL - 226
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 8
M1 - 107026
ER -