start-ver=1.4
cd-journal=joma
no-vol=46
cd-vols=
no-issue=1
article-no=
start-page=
end-page=
dt-received=
dt-revised=
dt-accepted=
dt-pub-year=2004
dt-pub=200401
dt-online=
en-article=
kn-article=
en-subject=
kn-subject=
en-title=
kn-title=Upper Cohen-Macaulay Dimension
en-subtitle=
kn-subtitle=
en-abstract=
kn-abstract=<p>In this paper, we define a homological invariant for finitely generated modules over a commutative noetherian local ring, which we call upper Cohen-Macaulay dimension. This invariant is quite similar to Cohen-Macaulay dimension that has been introduced by Gerko. Also we
define a homological invariant with respect to a local homomorphism of local rings. This invariant links upper Cohen-Macaulay dimension with Gorenstein dimension.</p>

en-copyright=
kn-copyright=

en-aut-name=ArayaTokuji
en-aut-sei=Araya
en-aut-mei=Tokuji
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=1
ORCID=

en-aut-name=TakahashiRyo
en-aut-sei=Takahashi
en-aut-mei=Ryo
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=2
ORCID=

en-aut-name=YoshinoYuji
en-aut-sei=Yoshino
en-aut-mei=Yuji
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=3
ORCID=

affil-num=1
en-affil=
kn-affil=Okayama University

affil-num=2
en-affil=
kn-affil=Okayama University

affil-num=3
en-affil=
kn-affil=Okayama University
en-keyword=Gorenstein dimension (G-dimension)
kn-keyword=Gorenstein dimension (G-dimension)
en-keyword= Cohen-Macaulay dimension (CM-dimension).
kn-keyword= Cohen-Macaulay dimension (CM-dimension).
END

start-ver=1.4
cd-journal=joma
no-vol=41
cd-vols=
no-issue=1
article-no=
start-page=
end-page=
dt-received=
dt-revised=
dt-accepted=
dt-pub-year=1999
dt-pub=199901
dt-online=
en-article=
kn-article=
en-subject=
kn-subject=
en-title=
kn-title=Nagata Criterion for Serre's (Rn) and (Sn)-Conditions
en-subtitle=
kn-subtitle=
en-abstract=
kn-abstract=
en-copyright=
kn-copyright=

en-aut-name=TakahashiRyo
en-aut-sei=Takahashi
en-aut-mei=Ryo
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=1
ORCID=

affil-num=1
en-affil=
kn-affil=Okayama University
END