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.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.