Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 53 1 2011 ABSTRACT LOCAL COHOMOLOGY FUNCTORS 129 154 EN Yuji Yoshino Takeshi Yoshizawa 10.18926/mjou/41402 We propose to define the notion of abstract local cohomology functors. The ordinary local cohomology functor RΓ_I with support in the closed subset defined by an ideal I and the generalized local cohomology functor RΓ_I,J 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 University Acta Medica Okayama 0030-1566 46 1 2004 Upper Cohen-Macaulay Dimension 17 30 EN Tokuji Araya Ryo Takahashi Yuji Yoshino 10.18926/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.