Quasi-socle ideals in local rings with Gorenstein tangent cones
Shiro Goto, Satoru Kimura, Naoyuki Matsuoka, and Tran Thi Phuo
Source: J. Commut. Algebra Volume 1, Number 4
(2009), 603-620.
First Page:
Show
Hide
Keywords: Quasi-socle ideal; regular local ring; Cohen-Macaulay ring; Gorenstein ring; associated graded ring; Rees algebra; Fiber cone; integral closure
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jca/1262962154
Digital Object Identifier: doi:10.1216/JCA-2009-1-4-603
Zentralblatt MATH identifier: 05673548
Mathematical Reviews number (MathSciNet): MR2575833
References
L. Burch, On ideals of finite homological dimension in local rings, Proc. Camb. Philos. Soc. 64 (1968), 941-948.
Mathematical Reviews (MathSciNet): MR229634
Digital Object Identifier: doi:10.1017/S0305004100043620
A. Corso, L. Ghezzhi, C. Polini and B. Ulrich, Cohen-Macaulayness of special fiber rings, Comm. Algebra 31 (2003), 3713-3734.
Mathematical Reviews (MathSciNet): MR2007381
Zentralblatt MATH: 1057.13007
Digital Object Identifier: doi:10.1081/AGB-120022439
A. Corso and C. Polini, Links of prime ideals and their Rees algebras, J. Algebra 178 (1995), 224-238.
Mathematical Reviews (MathSciNet): MR1358263
Zentralblatt MATH: 0848.13015
Digital Object Identifier: doi:10.1006/jabr.1995.1346
A. Corso and C. Polini, Reduction number of links of irreducible varieties, J. Pure Appl. Algebra 121 (1997), 29-43.
Mathematical Reviews (MathSciNet): MR1471122
Zentralblatt MATH: 0891.13008
Digital Object Identifier: doi:10.1016/S0022-4049(96)00042-4
T. Cortadellas and S. Zarzuela, On the Cohen-Macaulay property of the fiber cone of ideals with reduction number at most one, in Commutative algebra, algebraic geometry, and computational methods %(Hanoi, 1996), 215--222, Springer, Singapore, 1999.
Mathematical Reviews (MathSciNet): MR1714859
Zentralblatt MATH: 0945.13016
D. Eisenbud, Commutative algebra with a view toward algebraic geometry, Grad. Texts Math. 150, Springer-Verlag, New York, 1995.
Mathematical Reviews (MathSciNet): MR1322960
S. Goto and F. Hayasaka, Finite homological dimension and primes associated to integrally closed ideals, Proc. Amer. Math. Soc. 130 (2002), 3159-3164.
Mathematical Reviews (MathSciNet): MR1912992
Zentralblatt MATH: 0995.13009
Digital Object Identifier: doi:10.1090/S0002-9939-02-06436-5
JSTOR: links.jstor.org
S. Goto, S. Kimura and N. Matsuoka, Quasi-socle ideals in Gorenstein numerical semigroup rings, J. Algebra 320 (2008), 276-293.
Mathematical Reviews (MathSciNet): MR2417989
Digital Object Identifier: doi:10.1016/j.jalgebra.2008.01.015
S. Goto, N. Matsuoka, and Ryo Takahashi, Quasi-socle ideals in a Gorenstein local ring, J. Pure Appl. Algebra 212 (2008), 969-980.
Mathematical Reviews (MathSciNet): MR2387580
Zentralblatt MATH: 1137.13014
Digital Object Identifier: doi:10.1016/j.jpaa.2007.07.018
S. Goto and H. Sakurai, The equality $I^2=QI$ in Buchsbaum rings, Rend. Sem. Mat. Univ. Padova 110 (2003), 25-56.
Mathematical Reviews (MathSciNet): MR2033000
--------, The reduction exponent of socle ideals associated to parameter ideals in a Buchsbaum local ring of multiplicity two, J. Math. Soc. Japan 56 (2004), 1157-1168.
Mathematical Reviews (MathSciNet): MR2092942
Zentralblatt MATH: 1102.13003
Digital Object Identifier: doi:10.2969/jmsj/1190905453
Project Euclid: euclid.jmsj/1190905453
--------, When does the equality $I^2=QI$ hold true in Buchsbaum rings?, Commutative Algebra %115--139, Lecture Notes Pure Appl. Math. 244, 2006.
Zentralblatt MATH: 1098.13029
S. Goto and Y. Shimoda, On the Rees algebras of Cohen-Macaulay local rings, in Commutative algebra, %(Fairfax, Va., 1979), 201--231, Lecture Notes Pure Appl. Math. 68, Dekker, New York, 1982.
Mathematical Reviews (MathSciNet): MR655805
Zentralblatt MATH: 0482.13011
S. Goto and K. Watanabe, On graded rings I, J. Math. Soc. Japan, 30 (1978), 179-213; Proc. London Math. Soc. 29 (1974), 55-76.
Mathematical Reviews (MathSciNet): MR494707
Zentralblatt MATH: 0371.13017
Digital Object Identifier: doi:10.2969/jmsj/03020179
Project Euclid: euclid.jmsj/1240432552
R. Hübl and I. Swanson, Adjoints of ideals, arXiv:math.AC /0701071.
Mathematical Reviews (MathSciNet): MR2492462
Zentralblatt MATH: 1180.13005
Digital Object Identifier: doi:10.1307/mmj/1220879418
Project Euclid: euclid.mmj/1220879418
S. Ikeda, On the Gorensteinness of Rees algebras over local rings, Nagoya Math. J. 102 (1986), 135-154.
Mathematical Reviews (MathSciNet): MR846135
Zentralblatt MATH: 0585.13014
Project Euclid: euclid.nmj/1118780414
J. Lipman, Cohen-Macaulayness in graded algebras, Math. Res. Lett. 1 (1994), 149-157.
Mathematical Reviews (MathSciNet): MR1266753
Zentralblatt MATH: 0844.13006
D.G. Northcott and D. Rees, Reductions of ideals in local rings, Proc. Camb. Philos. Soc. 50 (1954), 145-158.
Mathematical Reviews (MathSciNet): MR59889
Digital Object Identifier: doi:10.1017/S0305004100029194
A. Ooishi, On the Gorenstein property of the associated graded ring and the Rees algebra of an ideal, J. Algebra 115 (1993), 397-414.
Mathematical Reviews (MathSciNet): MR1212236
Zentralblatt MATH: 0776.13004
Digital Object Identifier: doi:10.1006/jabr.1993.1051
C. Polini and B. Ulrich, Linkage and reduction numbers, Math. Ann. 310 (1998), 631-651.
Mathematical Reviews (MathSciNet): MR1619911
Zentralblatt MATH: 0919.13013
Digital Object Identifier: doi:10.1007/s002080050163
N.V. Trung and S. Ikeda, When is the Rees algebra Cohen-Macaulay?, Comm. Algebra 17 (1989), 2893-2922.
Mathematical Reviews (MathSciNet): MR1030601
Zentralblatt MATH: 0696.13015
Digital Object Identifier: doi:10.1080/00927878908823885
P. Valabrega and G. Valla, Form rings and regular sequences, Nagoya. Math. J. 72 (1978), 93-101.
Mathematical Reviews (MathSciNet): MR514892
Zentralblatt MATH: 0362.13007
Project Euclid: euclid.nmj/1118785674
H.-J. Wang, Links of symbolic powers of prime ideals, Math. Z. 256 (2007), 749-756.
Mathematical Reviews (MathSciNet): MR2308888
Zentralblatt MATH: 1123.13018
Digital Object Identifier: doi:10.1007/s00209-006-0099-7
J. Watanabe, The Dilworth number of Artin Gorenstein rings, Advances Math. 76 (1989), 194-199.
Mathematical Reviews (MathSciNet): MR1013668
Zentralblatt MATH: 0703.13019
Digital Object Identifier: doi:10.1016/0001-8708(89)90049-2
Journal of Commutative Algebra