Czechoslovak Mathematical Journal, online first, 9 pp.

On Buchsbaum type modules and the annihilator of certain local cohomology modules

Ahmad Khojali

Received June 16, 2016.   First published October 4, 2017.

Ahmad Khojali, Faculty of Sciences, University of Mohaghegh Ardabili, P. O. Box: 56199-11367, Ardabil, Iran, e-mail: khojali@uma.ac.ir, khojali@mail.com

Abstract: We consider the annihilator of certain local cohomology modules. Moreover, some results on vanishing of these modules will be considered.

Keywords: annihilator of local cohomology; non-Artinian local cohomology; Buchsbaum type module

Classification (MSC 2010): 13D45

DOI: 10.21136/CMJ.2017.0313-16

Full text available as PDF.


References:
[1] M. P. Brodmann, R. Y. Sharp: Local Cohomology. An Algebraic Introduction with Geometric Applications. Cambridge Studies in Advanced Mathematics 136, Cambridge University Press, Cambridge (2012). DOI 10.1017/CBO9781139044059 | MR 3014449 | Zbl 1263.13014
[2] W. Bruns, J. Herzog: Cohen-Macaulay Rings. Cambridge Studies in Advanced Mathematics 39, Cambridge University Press, Cambridge (1998). DOI 10.1017/CBO9780511608681 | Zbl 0909.13005
[3] W. Bruns, R. Schwänzl: The number of equations defining a determinantal variety. Bull. Lond. Math. Soc. 22 (1990), 439-445. DOI 10.1112/blms/22.5.439 | MR 1082012 | Zbl 0725.14039
[4] M. Eghbali: On Artinianness of formal local cohomology, colocalization and coassociated primes. Math. Scand. 113 (2013), 5-19. DOI 10.7146/math.scand.a-15478 | MR 3105540 | Zbl 1301.13019
[5] M. Eghbali, P. Schenzel: On an endomorphism ring of local cohomology. Commun. Algebra 40 (2012), 4295-4305. DOI 10.1080/00927872.2011.588982 | MR 2982939 | Zbl 1273.13027
[6] R. Hartshorne: Affine duality and cofiniteness. Invent. Math. 9 (1970), 145-164. DOI 10.1007/BF01404554 | MR 0257096 | Zbl 0196.24301
[7] M. Hellus: On the set of associated primes of a local cohomology module. J. Algebra 237 (2001), 406-419. DOI 10.1006/jabr.2000.8580 | MR 1813886 | Zbl 1027.13009
[8] M. Hellus: A note on the injective dimension of local cohomology modules. Proc. Am. Math. Soc. 136 (2008), 2313-2321. DOI 10.1090/S0002-9939-08-09198-3 | MR 2390497 | Zbl 1153.13015
[9] M. Hellus, J. Stückrad: On endomorphism rings of local cohomology modules. Proc. Am. Math. Soc. 136 (2008), 2333-2341. DOI 10.1090/S0002-9939-08-09240-X | MR 2390499 | Zbl 1152.13011
[10] M. Hochster, J. A. Eagon: A class of perfect determinantal ideals. Bull. Am. Math. Soc. 76 (1970), 1026-1029. DOI 10.1090/S0002-9904-1970-12543-5 | MR 0266912 | Zbl 0201.37201
[11] C. Huneke, J. Koh: Cofiniteness and vanishing of local cohomology modules. Math. Proc. Camb. Philos. Soc. 110 (1991), 421-429. DOI 10.1017/S0305004100070493 | MR 1120477 | Zbl 0749.13007
[12] C. Huneke, G. Lyubeznik: On the vanishing of local cohomology modules. Invent. Math. 102 (1990), 73-93. DOI 10.1007/BF01233420 | MR 1069240 | Zbl 0717.13011
[13] L. R. Lynch: Annihilators of top local cohomology. Commun. Algebra 40 (2012), 542-551. DOI 10.1080/00927872.2010.533223 | MR 2889480 | Zbl 1251.13015
[14] G. Lyubeznik: Finiteness properties of local cohomology modules (an application of $D$-modules to commutative algebra). Invent. Math. 113 (1993), 41-55. DOI 10.1007/BF01244301 | MR 1223223 | Zbl 0795.13004
[15] W. Mahmood, P. Schenzel: On invariants and endomorphism rings of certain local cohomology modules. J. Algebra 372 (2012), 56-67. DOI 10.1016/j.jalgebra.2012.08.023 | MR 2990000 | Zbl 1270.13014
[16] P. Schenzel: On formal local cohomology and connectedness. J. Algebra 315 (2007), 894-923. DOI 10.1016/j.jalgebra.2007.06.015 | MR 2351900 | Zbl 1131.13018
[17] J. Stückrad, W. Vogel: Buchsbaum Rings and Applications. An Interaction between Algebra, Geometry and Topology. Springer, Berlin (1986). DOI 10.1007/978-3-662-02500-0 | MR 0873945 | Zbl 0606.13017
[18] M. Varbaro: Cohomological and projective dimensions. Compos. Math. 149 (2013), 1203-1210. DOI 10.1112/S0010437X12000899 | MR 3078644 | Zbl 1290.13012


Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris.cz.
Subscribers of Springer need to access the articles on their site, which is http://link.springer.com/journal/10587.


[List of online first articles] [Contents of Czechoslovak Mathematical Journal] [Full text of the older issues of Czechoslovak Mathematical Journal at DML-CZ]