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A note on dimension of local cohomology modules | ||
| Journal of Algebra and Related Topics | ||
| دوره 13، شماره 2، اسفند 2025، صفحه 39-42 اصل مقاله (134.93 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.26183.1609 | ||
| نویسندگان | ||
| M. Amanalahzadeh1؛ J. Azami* 2؛ M. Shafiei3؛ I. Bagheriyeh4 | ||
| 1University of Mohaghegh Ardabili | ||
| 2Deprtment of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili | ||
| 3Payame noor University | ||
| 4Islamic Azad University | ||
| چکیده | ||
| Let $(R, m)$ be a commutative Noetherian local ring and $I$ be an ideal of $R$. In this paper first we find new results about the dimension of the local cohomology module $H^i_I(R)$. Then we will obtain new relations between the invariants such as arithmetic rank, cohomological dimension, krull dimension, and the height of an ideal of $R$. | ||
| کلیدواژهها | ||
| Associated primes؛ Krull dimension؛ Local cohomology | ||
| مراجع | ||
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[1] M. P. Brodmann and R.Y. Sharp, Local cohomology; an algebraic introduction with geometric applications, Cambridge University Press, Cambridge, 1998. [2] M. Dibaei and S. Yassemi, Attached primes of the topolocal cohomology modules with respect to an ideal, Archiv der Mathematik, 84 (2005), 292-297. [3] K. Divaani-Aazar, R. Naghipour and M. Tousi, Cohomological dimension of certain algebraic varieties, Proc. Amer. Math. Soc., 130 (2002), 3537–3544. [4] G. Faltings, Uber lokale Kohomologiegruppen hoher Ordnung, J. Reine Angew. Math., 313(1980), 43–51. [5] A. Grothendieck, Local Cohomology, Notes by R. Hartshorne, Lecture Notes in Math., 862 Springer, New York, 1966. [6] R. Hartshorne, Affine duality and cofiniteness, Invent. Math., 9 (1970), 145–164. [7] M. Hellus and J. Stuckrad, Matlis duals of top local cohomology modules, Proc. Amer. Math. Soc., 136 (2008), 489–498. [8] H. Matsumura, Commutative ring theory, Cambridge Univ. Press, Cambridge, UK, 1986. [9] A. A. Mehrvarz, K. Bahmanpour and R. Naghipour, Arithmetic rank, cohomological dimension and filter regular sequences, J. Alg. Appl., 8(2009), 855-862. [10] P. Schenzel, Proregular sequences, local cohomology, and completion, Math. Scand., 92 (2003), 161-180. | ||
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