Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664612004Upper Cohen-Macaulay Dimension1730ENTokujiArayaRyoTakahashiYujiYoshino10.18926/mjou/33917<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>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665312011ABSTRACT LOCAL COHOMOLOGY FUNCTORS129154ENYujiYoshinoTakeshiYoshizawa10.18926/mjou/41402We propose to define the notion of abstract local cohomology functors. The ordinary local cohomology functor RΓ<sub>I</sub> with support in the closed subset defined by an ideal I and the generalized local cohomology functor RΓ<sub>I,J</sub> defined in [16] are characterized as elements of the set of all the abstract local cohomology functors.No potential conflict of interest relevant to this article was reported.