start-ver=1.4
cd-journal=joma
no-vol=556
cd-vols=
no-issue=
article-no=
start-page=879
end-page=907
dt-received=
dt-revised=
dt-accepted=
dt-pub-year=2020
dt-pub=20200815
dt-online=
en-article=
kn-article=
en-subject=
kn-subject=
en-title=
kn-title=Constructing indecomposable integrally closed modules over a two-dimensional regular local ring
en-subtitle=
kn-subtitle=
en-abstract=
kn-abstract=In this article, we construct integrally closed modules of rank two over a two-dimensional regular local ring. The modules are explicitly constructed from a given complete monomial ideal with respect to a regular system of parameters. Then we investigate their indecomposability. As a consequence, we have a large class of indecomposable integrally closed modules whose Fitting ideal is not simple. This gives an answer to Kodiyalam's question.
en-copyright=
kn-copyright=

en-aut-name=HayasakaFutoshi
en-aut-sei=Hayasaka
en-aut-mei=Futoshi
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=1
ORCID=

affil-num=1
en-affil=Department of Environmental and Mathematical Sciences, Okayama University
kn-affil=
en-keyword=Integral closure
kn-keyword=Integral closure
en-keyword=Indecomposable module
kn-keyword=Indecomposable module
en-keyword=Monomial ideal
kn-keyword=Monomial ideal
en-keyword=Regular local ring
kn-keyword=Regular local ring
END

start-ver=1.4
cd-journal=joma
no-vol=226
cd-vols=
no-issue=8
article-no=
start-page=107026
end-page=
dt-received=
dt-revised=
dt-accepted=
dt-pub-year=2022
dt-pub=202208
dt-online=
en-article=
kn-article=
en-subject=
kn-subject=
en-title=
kn-title=Indecomposable integrally closed modules of arbitrary rank over a two-dimensional regular local ring
en-subtitle=
kn-subtitle=
en-abstract=
kn-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.
en-copyright=
kn-copyright=

en-aut-name=HayasakaFutoshi
en-aut-sei=Hayasaka
en-aut-mei=Futoshi
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=1
ORCID=

affil-num=1
en-affil=Department of Environmental and Mathematical Sciences, Okayama University
kn-affil=
en-keyword=integral closure
kn-keyword=integral closure
en-keyword=indecomposable module
kn-keyword=indecomposable module
en-keyword=monomial ideal
kn-keyword=monomial ideal
en-keyword=regular local ring
kn-keyword=regular local ring
END