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...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2017 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| 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| _version_ | 1862739080118272000 |
|---|---|
| author | Bhattacharyya, R. |
| author_facet | Bhattacharyya, R. |
| citation_txt | Flat extension and phantom homology / R. Bhattacharyya // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 1. — С. 90-98. — Бібліогр.: 10 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | 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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| first_indexed | 2025-12-07T20:07:10Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-156237 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T20:07:10Z |
| publishDate | 2017 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Bhattacharyya, R. 2019-06-18T10:16:30Z 2019-06-18T10:16:30Z 2017 Flat extension and phantom homology / R. Bhattacharyya // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 1. — С. 90-98. — Бібліогр.: 10 назв. — англ. 1726-3255 2010 MSC:13A35. https://nasplib.isofts.kiev.ua/handle/123456789/156237 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Flat extension and phantom homology Article published earlier |
| spellingShingle | Flat extension and phantom homology Bhattacharyya, R. |
| title | Flat extension and phantom homology |
| title_full | Flat extension and phantom homology |
| title_fullStr | Flat extension and phantom homology |
| title_full_unstemmed | Flat extension and phantom homology |
| title_short | Flat extension and phantom homology |
| title_sort | flat extension and phantom homology |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/156237 |
| work_keys_str_mv | AT bhattacharyyar flatextensionandphantomhomology |