A note on basic free modules and the condition.
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Let (A,M,K) denote a local noetherian ring A with maximal ideal M and residue field K. Let I be an ideal of A and E the Koszul complex generated over A by a system of generators of I.
The condition: H1(E) is a free A/I-module, appears in several important results of Commutative Algebra. For instance:
- (Gulliksen [3, Proposition 1.4.9]): The ideal I is generated by a regular sequence if and only if I has finite projective dimension and H
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