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...
Saved in:
| Date: | 2017 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2017
|
| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/41 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| id |
oai:ojs.admjournal.luguniv.edu.ua:article-41 |
|---|---|
| record_format |
ojs |
| spelling |
oai:ojs.admjournal.luguniv.edu.ua: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 |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2017-10-11T02:05:18Z |
| collection |
OJS |
| language |
English |
| topic |
tight closure phantom homology 13A35 |
| spellingShingle |
tight closure phantom homology 13A35 Bhattacharyya, Rajsekhar Flat extension and phantom homology |
| topic_facet |
tight closure phantom homology 13A35 |
| format |
Article |
| author |
Bhattacharyya, Rajsekhar |
| author_facet |
Bhattacharyya, Rajsekhar |
| author_sort |
Bhattacharyya, Rajsekhar |
| 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 |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2017 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/41 |
| work_keys_str_mv |
AT bhattacharyyarajsekhar flatextensionandphantomhomology |
| first_indexed |
2025-07-17T10:31:16Z |
| last_indexed |
2025-07-17T10:31:16Z |
| _version_ |
1837890135836852224 |