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Rees ring and integral closure of a filtration | ||
| Journal of Algebra and Related Topics | ||
| دوره 14، Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).، تیر 2026، صفحه 161-167 اصل مقاله (143.44 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2026.27565.1672 | ||
| نویسندگان | ||
| M. Yahyapour-Dakhel؛ F. Dorostkar* | ||
| Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran | ||
| چکیده | ||
| In this paper, we will study some properties of the integral closure of a filtration relative to a module in the Rees ring. | ||
| کلیدواژهها | ||
| Filtration؛ Integral closure of a filtration؛ Integral closure of a filtration relative to a module؛ Rees ring | ||
| مراجع | ||
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[1] N. Bourbaki, Elements of Mathematics, Commutative Algebra, Translated from the French, Hermann, Paris, 1972. [2] W. Bruns and J. Herzog, Cohen-Macaulay rings, Cambridge University Press, 1993. [3] H. Dichi, Integral dependence over a filtration, J. Pure Appl. Algebra, 58 (1989), 7-18. [4] H. Dichi, Integral closure of a filtration relative to a module, Comm. Algebra, (8) 23 (1995), 3145-3153. [5] H. Matsumura, Commutative Ring Theory, Cambridge University Press, 1980. [6] D. G. Northcott, Lessons on Rings, Modules and Multiplicities, Cambridge University Press, 1968. [7] D. G. Northcott and D. Rees, Reductions of ideals in local rings, Math. Proc. Cambridge Philos. Soc., (2) 50 (1954), 145-158. [8] J. S. Okon and L. J. Ratliff, Reductions of filtrations, Pacific J. Math., (1) 144 (1990), 137-154. [9] R. Y. Sharp, Y. Tiraş and M. Yassi, Integral closures of ideals relative to local cohomology modules over quasi-unmixed local rings, J. Lond. Math. Soc., (2) 42 (1990), 385-392. [10] Y. Tiraş, Integral closures of ideals in the Rees ring, Colloq. Math., (2) 64 (1993), 185-191. | ||
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