On sums of squares in local rings

@inproceedings{Scheiderer2001OnSO,
  title={On sums of squares in local rings},
  author={Claus Scheiderer},
  year={2001}
}
Let A be a semilocal ring. We compare the set of positive semidefinite (psd) elements of A and the set of sums of squares in A. For psd f ∈ A, whether f is a sum of squares or not depends only on the behavior of f in an infinitesimal neighborhood of the real zeros of f in Spec A. We apply this observation, first to 1-dimensional local rings, then to 2-dimensional regular semilocal rings. For the latter, we show that every psd element is a sum of squares. On the quantitative side, we obtain… CONTINUE READING

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