start-ver=1.4 cd-journal=joma no-vol=46 cd-vols= no-issue=1 article-no= start-page=17 end-page=30 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=

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.

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=53 cd-vols= no-issue=1 article-no= start-page=129 end-page=154 dt-received= dt-revised= dt-accepted= dt-pub-year=2011 dt-pub=201101 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=ABSTRACT LOCAL COHOMOLOGY FUNCTORS en-subtitle= kn-subtitle= en-abstract= kn-abstract=We propose to define the notion of abstract local cohomology functors. The ordinary local cohomology functor RΓI with support in the closed subset defined by an ideal I and the generalized local cohomology functor RΓI,J defined in [16] are characterized as elements of the set of all the abstract local cohomology functors. en-copyright= kn-copyright= en-aut-name=YoshinoYuji en-aut-sei=Yoshino en-aut-mei=Yuji kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= en-aut-name=YoshizawaTakeshi en-aut-sei=Yoshizawa en-aut-mei=Takeshi kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=2 ORCID= affil-num=1 en-affil= kn-affil=Graduate School of Natural Science and Technology Okayama University affil-num=2 en-affil= kn-affil=Graduate School of Natural Science and Technology Okayama University en-keyword=local cohomology kn-keyword=local cohomology en-keyword=stable t-structure kn-keyword=stable t-structure END