19,961 research outputs found
A Comment on the Positive Canons Project
Using the machinery of positive political theory in order to make some sense of legislative intent contains a number of provocative possibilities. Issues that require attention in this theory are addressed
On the growth of the Betti sequence of the canonical module
We study the growth of the Betti sequence of the canonical module of a
Cohen-Macaulay local ring. It is an open question whether this sequence grows
exponentially whenever the ring is not Gorenstein. We answer the question of
exponential growth affirmatively for a large class of rings, and prove that the
growth is in general not extremal. As an application of growth, we give
criteria for a Cohen-Macaulay ring possessing a canonical module to be
Gorenstein.Comment: 12 pages. version 2: includes omitted author contact informatio
Nonvanishing cohomology and classes of Gorenstein rings
We give counterexamples to the following conjecture of Auslander: given a
finitely generated module over an Artin algebra , there exists a
positive integer such that for all finitely generated -modules
, if \Ext_{\Lambda}^i(M,N)=0 for all , then
\Ext_{\Lambda}^i(M,N)=0 for all . Some of our examples moreover
yield homologically defined classes of commutative local rings strictly between
the class of local complete intersections and the class of local Gorenstein
rings.Comment: 16 page
- …