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On the asymptotic behaviour of associated primes of generalized local cohomology modules

Part of: General commutative ring theory Local theory Commutative algebra: Homological methods

Published online by Cambridge University Press:  09 April 2009

Kazem Khashyarmaneshs  and
Ahmad Abbasi
Kazem Khashyarmaneshs
Affiliation:
Fedowsi University of MashhadDepartment of MathematicsP.O. Box 1159–91775Mashhad Iran and Institute for Studies in Theoretical Physics and MathematicsP.O. Box 19395–5746TehranIrankhashyar@ipm.ir
Ahmad Abbasi
Affiliation:
Guilan UniversityDepartment of MathematicsP.O. Box 41335–1914RashtIran, aabbasi@guilan.ac.ir
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Abstract

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Let M and N be finitely generated and graded modules over a standard positive graded commutative Noetherian ring R, with irrelevant ideal R+. Let be the nth component of the graded generalized local cohomology module . In this paper we study the asymptotic behavior of Assf R+ () as n → –∞ whenever k is the least integer j for which the ordinary local cohomology module is not finitely generated.

MSC classification

Secondary: 13D45: Local cohomology 13A02: Graded rings 14B15: Local cohomology

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 83 , Issue 2 , October 2007 , pp. 217 - 226
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Asadollahi, J., Khashyarmanesh, K. and Salarian, Sh., ‘On the finiteness properties of the generalized local cohomology modules’, Comm. Algebra 30 (2002), 859–867.Google Scholar
[2]Bijan-Zadeh, M. H., ‘A common generalization of local cohomology theories’, Glasg. Math. J. 21 (1980), 173–181.CrossRefGoogle Scholar
[3]Brodmann, M., ‘Asymptotic behaviour of cohomology: tameness, supports and associated primes’, in: Commutative algebra and algebraic geometry, Contemp. Math. 390 (Amer. Math. Soc, Providence, RI, 2005) pp. 31–61.CrossRefGoogle Scholar
[4]Brodmann, M., Fumasoli, S. and Lim, C. S., ‘Low-codimensional associated primes of graded components of local cohomology modules’, J. Algebra 275 (2004), 867–882.Google Scholar
[5]Brodmann, M., Fumasoli, S. and Tajarod, R., ‘Local cohomology over homogeneous rings with one-dimensional local bast ring’, Proc. Amer. Math. Soc. 131 (2003), 2977–2985.Google Scholar
[6]Brodmann, M. and Hellus, M., ‘Cohomological patterns of coherent sheaves over projective schemes’, J. Pure Appl. Alyebra 172 (2002), 165–182.Google Scholar
[7]Brodmann, M., Katzman, M. and Sharp, R. Y., ‘Associated primes of graded components of local cohomology modules’, Trans. Amer. Math. Soc. 354 (2002), 4261–4283.CrossRefGoogle Scholar
[8]Brodmann, M. and Sharp, R. Y., Local cohomology an algebraic introduction with geometric applications, volume 60 of Cambridge studies in advanced mathematics (Cambridge University Press, 1998).Google Scholar
[9]Bruns, W. and Herzog, J., Cohen-Macaulay rings, volume 39 of Cambridge studies in advanced mathematics (Cambridge University Press, 1993).Google Scholar
[10]Herzog, J., ‘Komplexe, auflösungen und dualität in der lokalen algebra’, Preprint ????, 1974.Google Scholar
[11]Herzog, J. and Zamani, N., ‘Duality and vanishing of generalized local cohomology’, Arch. Math. (Basel) 81 (2003), 512–519.Google Scholar
[12]Huckaba, S. and Marley, T., ‘On associated graded rings of normal ideals’, J. Algebra 222 (1999), 146–163.Google Scholar
[13]Katzman, M. and Sharp, R. Y., ‘Some properties of top graded local cohomology modules’, J. Algebra 259 (2003), 599–612.CrossRefGoogle Scholar
[14]Khashyarmanesh, K., ‘Associated primes of graded components of gneralized local cohomology modules’, Comm. Algebra 33 (2005), 3081–3090.CrossRefGoogle Scholar
[15]Khashyarmanesh, K. and Salarian, Sh., ‘Filter regular sequences and the finiteness of local cohomology modules’, Comm. Algebra 26 (1998), 2483–2490.CrossRefGoogle Scholar
[16]Khashyarmanesh, K., Yassi, M. and Abbasi, A., ‘Filter regular sequences and generalized local cohomology modules’, Comm. Algebra 32 (2004), 253–259.Google Scholar
[17]Lim, C. S., ‘Graded local cohomology modules and their associated primes: the Cohen-Macaulay case’, J. Pure Appl. Algebra 185 (2003), 225–238.Google Scholar
[18]Lim, C. S., ‘Graded local cohomology modules and their associated primes’, Comm. Algebra 32 (2004), 727–745.Google Scholar
[19]Matsumura, H., Commutative Ring Therory, volume 8 of Cambridge studies in advanced mathematics (Cambridge University Press, 1986).Google Scholar
[20]Nagel, U. and Schenzel, P., ‘Cohomological annihilators and Castelnuovo-Mumford regularity’, in: Commutative algebra: syzygies, multiplicities, and birational algebra (South Hadley, MA, 1992), Contemp. Math. 159 (Amer. Math. Soc, Providence, RI, 1994) pp. 307–328.Google Scholar
[21]Suzuki, N., ‘On the generalized local cohomology and its duality’, J. Math. Kyoto Univ. (JAKYAZ) 18–1 (1978), 71–85.Google Scholar
[22]Yassemi, S., ‘Generalized section functor’, J. Pure Appl. Algebra 95 (1994), 103–119.Google Scholar
[23]Yassemi, S., Khatami, L. and Sharif, T., ‘Associated primes of generalized local cohomology modules’, Comm. Algebra 30 (2002), 327–330.CrossRefGoogle Scholar