Flat extension and phantom homology

Rajsekhar Bhattacharyya


Phantom homology arises in tight closure theory due to small non-exactness when `kernel' is not equal to `image' but `kernel' is in the tight closure of the `image'. In this paper we study a typical flat extension, which we call *-flat extension, such that upon tensoring which preserves phantom homology. Along with other properties, we observe that *-flat extension preserves ghost regular sequence, which is a typical `tight closure' generalization of regular sequence. We also show that in some situations, under *-flat extension, test ideal of the *-flat algebra is the expansion of the test ideal of the base ring.


tight closure, phantom homology

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