Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
annihilator of local cohomology; non-Artinian local cohomology; Buchsbaum type module
annihilator of local cohomology; non-Artinian local cohomology; Buchsbaum type module
Summary:
We consider the annihilator of certain local cohomology modules. Moreover, some results on vanishing of these modules will be considered.
References:
[1] Brodmann, M. P., Sharp, R. Y.: 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] Bruns, W., Herzog, J.: Cohen-Macaulay Rings. Cambridge Studies in Advanced Mathematics 39, Cambridge University Press, Cambridge (1998). DOI 10.1017/CBO9780511608681 | MR 1251956 | Zbl 0909.13005
[3] Bruns, W., Schwänzl, R.: 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] Eghbali, M.: 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] Eghbali, M., Schenzel, P.: 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] Hartshorne, R.: Affine duality and cofiniteness. Invent. Math. 9 (1970), 145-164. DOI 10.1007/BF01404554 | MR 0257096 | Zbl 0196.24301
[7] Hellus, M.: 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] Hellus, M.: 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] Hellus, M., Stückrad, J.: 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] Hochster, M., Eagon, J. A.: 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] Huneke, C., Koh, J.: 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] Huneke, C., Lyubeznik, G.: On the vanishing of local cohomology modules. Invent. Math. 102 (1990), 73-93. DOI 10.1007/BF01233420 | MR 1069240 | Zbl 0717.13011
[13] Lynch, L. R.: Annihilators of top local cohomology. Commun. Algebra 40 (2012), 542-551. DOI 10.1080/00927872.2010.533223 | MR 2889480 | Zbl 1251.13015
[14] Lyubeznik, G.: 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] Mahmood, W., Schenzel, P.: 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] Schenzel, P.: 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] Stückrad, J., Vogel, W.: 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] Varbaro, M.: Cohomological and projective dimensions. Compos. Math. 149 (2013), 1203-1210. DOI 10.1112/S0010437X12000899 | MR 3078644 | Zbl 1290.13012
Search
Partner of
