Geodesic
Flat extension and phantom homology
Algebra and discrete mathematics, Tome 24 (2017) no. 1, pp. 90-98

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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.
Keywords: tight closure, phantom homology. 
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     author = {Rajsekhar Bhattacharyya},
     title = {Flat extension and phantom homology},
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     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2017_24_1_a5/}
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Rajsekhar Bhattacharyya. Flat extension and phantom homology. Algebra and discrete mathematics, Tome 24 (2017) no. 1, pp. 90-98. http://geodesic.mathdoc.fr/item/ADM_2017_24_1_a5/