Abstract
We present a constructive solution of the inverse syzygy problem over arbitrary coherent rings. By relating the existence of a kernel representation to torsionlessness instead of the more common torsionfreeness, we do not need to assume the existence of a quotient field. As a by-product, we obtain an algorithm to compute the extension groups of finitely presented modules.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENT
This article is cordially dedicated to Ulrich Oberst on the occasion of his retirement in 2009.
Notes
Note that Auslander and Bridger speak of k-torsionfree modules, but their notion of 1-torsionfree is equivalent to what we call torsionless.
In the case of a commutative ring 𝒟, we may of course use the more common realisation β(m) = Bm and obtain then β*(x) = B t x, where B t denotes the transposed matrix.
Communicated by M. Cohen.