MAPS BETWEEN NON-COMMUTATIVE SPACES (vol 356, pg 2927, 2004)

The statement of Lemma 3.1 in Maps between non-commutative spaces (Trans. Amer. Math. Soc. 356 (2004), no. 7, 2927-2944) is not correct. Lemma 3.1 is needed for the proof of Theorem 3.2. Theorem 3.2 as originally stated is true but its "proof" is not correct. Here we change the statements and proofs of Lemma 3.1 and Theorem 3.2. We also prove a new result. Let k be a field, A a left and right noetherian N-graded k-algebra such that dim(k)(A(n)) < infinity for all n, and J a graded two-sided ideal of A. If the noncommutative scheme Proj(nc)(A) is isomorphic to a projective scheme X, then there is a closed subscheme Z subset of X such that Proj(nc)(A/J) is isomorphic to Z. This result is a geometric translation of what we actually prove: if the category QGr(A) is equivalent to Qcoh(X), then QGr(A/J) is equivalent to Qcoh(Z) for some closed subscheme Z subset of X.