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The conjecture of Wolmer Vasconcelos on the vanishing of the first Hilbert coefficient  e  1 ( Q ) is solved affirmatively, where  Q  is a parameter ideal in a Noetherian local ring. Basic properties of the rings for which  e  1 ( Q ) vanishes are derived. The invariance of  e  1 ( Q ) for parameter ideals  Q  and its relationship to Buchsbaum rings are studied.

Cohen–Macaulayness versus the vanishing of the first Hilbert coefficient of parameter ideals