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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| Дата: | 2017 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2017
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.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| id |
irk-123456789-156237 |
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dspace |
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irk-123456789-1562372019-06-19T01:27:18Z Flat extension and phantom homology Bhattacharyya, R. 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. 2017 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/156237 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Bhattacharyya, R. |
| spellingShingle |
Bhattacharyya, R. Flat extension and phantom homology Algebra and Discrete Mathematics |
| author_facet |
Bhattacharyya, R. |
| author_sort |
Bhattacharyya, R. |
| title |
Flat extension and phantom homology |
| title_short |
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_sort |
flat extension and phantom homology |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/156237 |
| citation_txt |
Flat extension and phantom homology / R. Bhattacharyya // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 1. — С. 90-98. — Бібліогр.: 10 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT bhattacharyyar flatextensionandphantomhomology |
| first_indexed |
2023-05-20T17:49:14Z |
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2023-05-20T17:49:14Z |
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1796154166370893824 |