| Title:
|
The torsion theory and the Melkersson condition (English) |
| Author:
|
Yoshizawa, Takeshi |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
121-145 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider a generalization of the notion of torsion theory, which is associated with a Serre subcategory over a commutative Noetherian ring. In 2008 Aghapournahr and Melkersson investigated the question of when local cohomology modules belong to a Serre subcategory of the module category. In their study, the notion of Melkersson condition was defined as a suitable condition in local cohomology theory. One of our purposes in this paper is to show how naturally the concept of Melkersson condition appears in the context of torsion theories. (English) |
| Keyword:
|
Melkersson condition |
| Keyword:
|
Serre subcategory |
| Keyword:
|
torsion theory |
| MSC:
|
13C60 |
| MSC:
|
13D30 |
| idZBL:
|
07217124 |
| idMR:
|
MR4078349 |
| DOI:
|
10.21136/CMJ.2019.0193-18 |
| . |
| Date available:
|
2020-03-10T10:15:39Z |
| Last updated:
|
2022-04-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148045 |
| . |
| Reference:
|
[1] Aghapournahr, M., Melkersson, L.: Local cohomology and Serre subcategories.J. Algebra 320 (2008), 1275-1287. Zbl 1153.13014, MR 2427643, 10.1016/j.jalgebra.2008.04.002 |
| Reference:
|
[2] Beligiannis, A., Reiten, I.: Homological and homotopical aspects of torsion theories.Mem. Am. Math. Soc. 883 (2007), 207 pages. Zbl 1124.18005, MR 2327478, 10.1090/memo/0883 |
| Reference:
|
[3] Dickson, S. E.: A torsion theory for Abelian categories.Trans. Am. Math. Soc. 121 (1966), 223-235. Zbl 0138.01801, MR 0191935, 10.2307/1994341 |
| Reference:
|
[4] Gabriel, P.: Des catégories abéliennes.Bull. Soc. Math. Fr. 90 (1962), 323-448 French. Zbl 0201.35602, MR 0232821, 10.24033/bsmf.1583 |
| Reference:
|
[5] Lambek, J.: Torsion Theories, Additive Semantics, and Rings of Quotients.Lecture Notes in Mathematics 177, Springer, Berlin (1971). Zbl 0213.31601, MR 0284459, 10.1007/BFb0061029 |
| Reference:
|
[6] Stenström, B.: Rings and Modules of Quotients.Lecture Notes in Mathematics 237, Springer, Berlin (1971). Zbl 0229.16003, MR 0325663, 10.1007/BFb0059904 |
| Reference:
|
[7] Stenström, B.: Rings of Quotients. An Introduction to Methods of Ring Theory.Die Grundlehren der Mathematischen Wissenschaften 217, Springer, Berlin (1975). Zbl 0296.16001, MR 0389953, 10.1007/978-3-642-66066-5 |
| Reference:
|
[8] Yoshizawa, T.: Subcategories of extension modules by Serre subcategories.Proc. Am. Math. Soc. 140 (2012), 2293-2305. Zbl 1273.13018, MR 2898693, 10.1090/S0002-9939-2011-11108-0 |
| Reference:
|
[9] Yoshizawa, T.: On the closedness of taking injective hulls of several Serre subcategories.Commun. Algebra 45 (2017), 4846-4854. Zbl 1390.13040, MR 3670355, 10.1080/00927872.2017.1284226 |
| . |
