Local homology and Serre categories
cytuj
pobierz pliki
RIS BIB ENDNOTEWybierz format
RIS BIB ENDNOTELocal homology and Serre categories
Data publikacji: 17.12.2019
Universitatis Iagellonicae Acta Mathematica, 2019, Tom 56, s. 7 - 14
https://doi.org/10.4467/20843828AM.19.001.12109Autorzy
Local homology and Serre categories
We show some results about local homology modules when they are in a Serre subcategory of the category of R-modules. For an ideal a of R, we also define the concept of the condition Ca on a Serre category, which seems dual to the condition Ca in Melkersson [1]. As a main result we show that for an Artinian R-module M and any Serre subcategory S of the category of R-modules and a non-negative integer s, HomR(R/a,Has (M)) ∈ S if Hai (M) ∈ S for all i > s.
2010 Mathematics Subject Classification. 13D45, 13M10; 13E15.
1. Aghapournahr M., Melkersson L., Local cohomology and Serre subcategories, J. Algebra, 320 (2008), 1275–1287.
2. Asgharzadeh M., Tousi M., A unified approach to local cohomology modules using Serre classes, Canadian Math. Bull., 53(1) (2010), 1–10.
3. Brodmann M., Sharp R.Y., Local cohomology, an algebraic introduction with geometric applications, Cambridge Univ. Press, Cambridge, 1998.
4. Cuong N.T., Nam T.T., The I-adic completion and local homology for Artinian modules, Math. Proc. Camb. Philos. Soc., 131 (2001), 61–72.
5. Cuong N.T., Nam T. T., A local homology theory for linearly compact modules, J. Algebra, 319 (2008), 4712–4737.
6. Greenlees J.P.C., May J.P., Derived functors of I-adic completion and local homology, J. Algebra, 149 (1992), 438–453.
7. Grothendieck A., Local Cohomology, Springer-Verlag, Berlin, Tokyo, New York, 1967.
8. Hartshorne R., Affne duality and cofiniteness, Invent. Math., 9 (1970), 14–164.
9. Kirby D., Dimension and length for Artinian modules, Quart. J. Math., 41(2) (1990), 419–429.
10. Macdonald I.G., Duality over complete local rings, Topology, 1 (1962), 213–235.
11. Melkersson L., Schenzel P., The co-localization of an Artinian module, Proc. Edinburgh Math. Soc., 38 (1995), 121–131.
12. Nam T.T., Cosupport and coartinian modules, Algebra Colloq., 15(1) (2008), 83–96.
13. Nam T.T., Minimax modules, local homology and local cohomology, International Jornal of Mathematices., 26(12) (2015).
14. Roberts R.N., Krull dimension for Artinian modules over quasi local commutative rings, Quart. J. Math., 26(3) (1975), 269–273.
15. Yassemi S., Coassociated primes, Comm. Algebra, 23(4) (1995), 1473–1498.
Informacje: Universitatis Iagellonicae Acta Mathematica, 2019, Tom 56, s. 7 - 14
Typ artykułu: Oryginalny artykuł naukowy
Tytuły:
Local homology and Serre categories
Local homology and Serre categories
Department of Mathematics, Payam Noor University, Tehran, Iran
Department of Mathematics, Payam Noor University, Tehran, Iran
Publikacja: 17.12.2019
Otrzymano: 30.09.2018
Status artykułu: Otwarte
Licencja: CC BY-NC-ND
Udział procentowy autorów:
Korekty artykułu:
-Języki publikacji:
Angielski