The Cohen-Macaulayness of the Rees algebras of local rings

Shin Ikeda

Type: Article

Publication Date: 1983-03-01

Citations: 13

DOI: https://doi.org/10.1017/s0027763000020237

Abstract

Let (A, m, k) be a Noetherian local ring. We define and call it the Rees algebra of A . Let X be an indeterminate over A , then R ( A ) can be identified with the A -subalgebra .

Locations

Nagoya Mathematical Journal - View - PDF
Project Euclid (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	On the Gorensteinness of Rees algebras over local rings	1986	Shin Ikeda
+	Rees Modules and Reduction of an Ideal Relative to a Noetherian Module	2011	Naser Zamani
+ PDF Chat	Coefficient ideals and the Cohen-Macaulay property of Rees algebras	2000	Eero Hyry
+	The Rees Algebra of a Module and Ideal Module over Noetherian Local Ring	2012	Priti Singh Shiv Datt Kumar
+	On arithmetic macaulayfication of certain local rings	1998	Takesi Kawasaki
+	LOCALLY COMPLETE INTERSECTION IDEALS IN COHEN-MACAULAY LOCAL RINGS	1994	Mee-Kyoung Kim
+	Quasi-Gorensteinness of extended Rees algebras	2013	Youngsu Kim
+	A note on the cohen-macaulayness of multi-rees rings	1999	Zhongming Tang
+ PDF Chat	Quasi-Gorensteinness of extended Rees algebras	2017	Youngsu Kim
+	On the Cohen-Macaulayness and defining ideal of Rees algebras of modules	2018	Alessandra Costantini
+	On the Cohen-Macaulay property of the Rees algebra of the module of differentials	2020	Alessandra Costantini Tan Dang
+ PDF Chat	Remarks on lifting of Cohen-Macaulay property	1983	Manfred Herrmann Shin Ikeda
+	On Cohen-Macaulay and Gorenstein properties of Rees algebras	1994	幸男中村
+ PDF Chat	Cohen–Macaulayness of Rees Algebras of Modules	2016	Kuei-Nuan Lin
+ PDF Chat	Rees algebras of ideals having small analytic deviation	1993	Sam Huckaba Craig Huneke
+	On the Gorensteinness of Rees algebras over local rings	1985	信池田
+	Rees algebra over an ideal in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="fraktur">t</mml:mi></mml:math>-rings	2014	Jyoti Singh Shiv Datt Kumar
+	Results on Generalization of Burch’s Inequality and the Depth of Rees Algebra and Associated Graded Rings of an Ideal with Respect to a Cohen-Macaulay Module	2018	Mohadeseh Tohidi Амир Мафи Kamal Ahmadi
+ PDF Chat	Reduction Numbers and Rees Algebras of Powers of an Ideal	1993	Lê Tuâń Hoa
+	On arithmetic Macaulayfication of Noetherian rings	2001	Takesi Kawasaki

Works That Cite This (13)

Action	Title	Year	Authors
+ PDF Chat	On the Gorensteinness of Rees algebras over local rings	1986	Shin Ikeda
+ PDF Chat	Affine Semigroups and Cohen-Macaulay Rings Generated by Monomials	1986	Ngô Viêt Trung Lê Tuâń Hoa
+ PDF Chat	Affine semigroups and Cohen-Macaulay rings generated by monomials	1986	Ngô Viêt Trung Lê Tuâń Hoa
+	When is the rees algebra cohen—macaulay?	1989	t Trung NgôViê Shin Ikeda
+	Graded Cohen-Macaulay rings associated to equimultiple ideals	1984	U. Grothe Manfred Herrmann Ulrich Orbanz
+	Depth Formulas For Certain Graded Modules Associated To A Filtration	2001	Santiago Zarzuela Teresa Cortadellas
+	Type of blowing-up over a Buchsbaum ring	1994	Kikumichi Yamagishi
+	On the depth of the canonical modules of graded rings associated to an ideal	2000	Teresa Cortadellas
+ PDF Chat	Remarks on lifting of Cohen-Macaulay property	1983	Manfred Herrmann Shin Ikeda
+ PDF Chat	On certain $d$-sequence on Rees algebra	1987	Yasuhiro Shimoda

Works Cited by This (9)

Action	Title	Year	Authors
+ PDF Chat	Eine Verallgemeinerung der Cohen-Macaulay Ringe und Anwendungen auf ein Problem der Multiplizitätstheorie	1973	Jürgen Stückrad Wolfgang Vogel
+ PDF Chat	A conjecture of Nagata on graded Cohen-Macaulay rings	1974	Jacob Matijevic Paul Roberts
+	On Rees algebras over Buchsbaum rings	1980	Shirô Gotô Yasuhiro Shimoda
+	Applications of dualizing complexes to Buchsbaum rings	1982	Peter Schenzel
+	Weitere Bemerkungen zu einem problem der Schnittheorie und über ein Maβ von A. Seidenberg für die Imperfektheit	1975	Bodo Renschuch Jürgen Stückrad Wolfgang Vogel
+	Certain graded algebras are always Cohen-Macaulay	1976	Giuseppe Valla
+	Reductions of ideals in local rings	1954	D. G. Northcott D. Andrew S. Rees
+	Verallgemeinerte COHEN-MACAULAY-Moduln	1978	Peter Schenzel Ngô Viêt Trung Nguyen Tu Cuong
+	Codimension and Multiplicity	1958	Maurice Auslander David A. Buchsbaum