Flat extension and phantom homology
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 pr...
Збережено в:
| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2017 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2017
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/156237 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Flat extension and phantom homology / R. Bhattacharyya // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 1. — С. 90-98. — Бібліогр.: 10 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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.
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| ISSN: | 1726-3255 |