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top-method

If M is a module in a polynomial ring R, then the implementations of top and removeLowestDimension are based on the following observations:

  • codim Ext^d(M,R) >= d, for all d (if the module is non-zero)
  • If P is an associated prime of M of codimension d := codim P > codim M, then codim Ext^d(M,R) = d and the annihilator of Ext^d(M,R) is contained in P
  • If codim Ext^d(M,R) = d, then there really is an associated prime of codimension d.
  • If M is R/I, then top(I) = ann Ext^c(R/I,R), where c = codim I

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