The torsion theory and the Melkersson condition

Takeshi Yoshizawa

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 1, page 121-145
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Yoshizawa, Takeshi. "The torsion theory and the Melkersson condition." Czechoslovak Mathematical Journal 70.1 (2020): 121-145. <http://eudml.org/doc/296955>.

@article{Yoshizawa2020,
abstract = {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.},
author = {Yoshizawa, Takeshi},
journal = {Czechoslovak Mathematical Journal},
keywords = {Melkersson condition; Serre subcategory; torsion theory},
language = {eng},
number = {1},
pages = {121-145},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The torsion theory and the Melkersson condition},
url = {http://eudml.org/doc/296955},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Yoshizawa, Takeshi
TI - The torsion theory and the Melkersson condition
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 1
SP - 121
EP - 145
AB - 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.
LA - eng
KW - Melkersson condition; Serre subcategory; torsion theory
UR - http://eudml.org/doc/296955
ER -

References

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  1. Aghapournahr, M., Melkersson, L., 10.1016/j.jalgebra.2008.04.002, J. Algebra 320 (2008), 1275-1287. (2008) Zbl1153.13014MR2427643DOI10.1016/j.jalgebra.2008.04.002
  2. Beligiannis, A., Reiten, I., 10.1090/memo/0883, Mem. Am. Math. Soc. 883 (2007), 207 pages. (2007) Zbl1124.18005MR2327478DOI10.1090/memo/0883
  3. Dickson, S. E., 10.2307/1994341, Trans. Am. Math. Soc. 121 (1966), 223-235. (1966) Zbl0138.01801MR0191935DOI10.2307/1994341
  4. Gabriel, P., 10.24033/bsmf.1583, Bull. Soc. Math. Fr. 90 (1962), 323-448 French. (1962) Zbl0201.35602MR0232821DOI10.24033/bsmf.1583
  5. Lambek, J., 10.1007/BFb0061029, Lecture Notes in Mathematics 177, Springer, Berlin (1971). (1971) Zbl0213.31601MR0284459DOI10.1007/BFb0061029
  6. Stenström, B., 10.1007/BFb0059904, Lecture Notes in Mathematics 237, Springer, Berlin (1971). (1971) Zbl0229.16003MR0325663DOI10.1007/BFb0059904
  7. Stenström, B., 10.1007/978-3-642-66066-5, Die Grundlehren der Mathematischen Wissenschaften 217, Springer, Berlin (1975). (1975) Zbl0296.16001MR0389953DOI10.1007/978-3-642-66066-5
  8. Yoshizawa, T., 10.1090/S0002-9939-2011-11108-0, Proc. Am. Math. Soc. 140 (2012), 2293-2305. (2012) Zbl1273.13018MR2898693DOI10.1090/S0002-9939-2011-11108-0
  9. Yoshizawa, T., 10.1080/00927872.2017.1284226, Commun. Algebra 45 (2017), 4846-4854. (2017) Zbl1390.13040MR3670355DOI10.1080/00927872.2017.1284226

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