Non-Cohen-Macaulay unique factorization domains in small dimensions
We construct examples of non-Cohen-Macaulay unique factorization domains in small dimension. We find a unique factorization domain of dimension 3 which is not a Cohen-Macaulay ring. Moreover, there is an example of a five-dimensional affine ring S over a field k with the property that S is a non-Cohen-Macaulay unique factorization domain whenever Char k = 2, while it is a Gorenstein non-factorial ring for Char k not equal 2. The arguments for the proofs are conceptional as well as based on a Computer Algebra System like SINGULAR or MACAULAY. For the theoretical background we investigate the factorial closure of the symmetric algebra of certain monomial modules. (C) 2010 Elsevier Ltd. All rights reserved.
cohen-macaulay ring factorial closure factorial ring