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 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2017
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/41 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543151764799488 |
|---|---|
| author | Bhattacharyya, Rajsekhar |
| author_facet | Bhattacharyya, Rajsekhar |
| author_sort | Bhattacharyya, Rajsekhar |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2017-10-11T02:05:18Z |
| 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. |
| first_indexed | 2026-02-08T07:57:55Z |
| format | Article |
| id | admjournalluguniveduua-article-41 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:57:55Z |
| publishDate | 2017 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-412017-10-11T02:05:18Z Flat extension and phantom homology Bhattacharyya, Rajsekhar tight closure, phantom homology 13A35 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. Lugansk National Taras Shevchenko University 2017-10-07 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/41 Algebra and Discrete Mathematics; Vol 24, No 1 (2017) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/41/pdf Copyright (c) 2017 Algebra and Discrete Mathematics |
| spellingShingle | tight closure phantom homology 13A35 Bhattacharyya, Rajsekhar Flat extension and phantom homology |
| 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 |
| topic | tight closure phantom homology 13A35 |
| topic_facet | tight closure phantom homology 13A35 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/41 |
| work_keys_str_mv | AT bhattacharyyarajsekhar flatextensionandphantomhomology |