Abstract

In this paper, we consider the openness of the P-locus of a finitely generated module over a commutative noetherian ring in the case where P is each of the properties FID, Gor, Can, CM, MCM, (Sn), and (Tn). One of the main results asserts that FID-loci over an acceptable ring are open. We give a module version of the Nagata criterion, and prove that it holds for all of the aforementioned properties.

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