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Agustin Marcelo 《Journal of Symbolic Computation》2011,46(5):609-621
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≠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. 相似文献
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