ABSTRACT
The aim of this paper is to show that the property for a module having G-dimension 0 is an “open” property. To be more precise, let R be a Noetherian commutative algebra over a field k and let M and N be finitely generated R-modules. Suppose that N is a degeneration of M in some sense. Then we shall prove the inequality G-dimM G-dimN in Theorem (3.2). In particular, that G-dimN 0 implies that G-dimM 0 in this case. We infer from this that if there are some moduli spaces of finitely generated R-modules, then the set of modules with Gdimension 0 should form an open subset.
