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A property of ideals in polynomial rings
Author:
Gennady Lyubeznik
Journal:
Proc. Amer. Math. Soc. 98 (1986), 399-400
MSC:
Primary 13C05
MathSciNet review:
857929
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Abstract: Every ideal in the polynomial ring in  variables over an infinite field has a reduction generated by  elements.
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Lindsay
Burch, Codimension and analytic spread, Proc. Cambridge
Philos. Soc. 72 (1972), 369–373. MR 0304377
(46 #3512)
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David
Eisenbud and E.
Graham Evans Jr., Every algebraic set in 𝑛-space is the
intersection of 𝑛\
hypersurfaces, Invent. Math.
19 (1973), 107–112. MR 0327783
(48 #6125)
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David
Eisenbud and E.
Graham Evans Jr., Generating modules efficiently: theorems from
algebraic 𝐾-theory, J. Algebra 27 (1973),
278–305. MR 0327742
(48 #6084)
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N.
Mohan Kumar, On two conjectures about polynomial rings,
Invent. Math. 46 (1978), no. 3, 225–236. MR 499785
(80c:13010), http://dx.doi.org/10.1007/BF01390276
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S.
Mandal, On efficient generation of ideals, Invent. Math.
75 (1984), no. 1, 59–67. MR 728138
(85d:13017), http://dx.doi.org/10.1007/BF01403089
- [6]
D.
G. Northcott and D.
Rees, Reductions of ideals in local rings, Proc. Cambridge
Philos. Soc. 50 (1954), 145–158. MR 0059889
(15,596a)
- [7]
Avinash
Sathaye, On the Forster-Eisenbud-Evans conjectures, Invent.
Math. 46 (1978), no. 3, 211–224. MR 499784
(80c:13009), http://dx.doi.org/10.1007/BF01390275
- [1]
- L. Burch, Codimension and analytic spread, Proc. Cambridge Philos. Soc. 72 (1972), 369-373. MR 0304377 (46:3512)
- [2]
- D. Eisenbud and E. Evans, Every algebraic set in
 -space is a set-theoretic intersection of  hypersurfaces, Invent. Math. 19 (1973), 107-112. MR 0327783 (48:6125)
- [3]
- -, Generating modules efficiently: Theorems from algebraic
 -theory, J. Algebra 27 (1973), 278-305. MR 0327742 (48:6084)
- [4]
- Mohan Kumar, On two conjectures about polynomial rings, Invent. Math. 46 (1978), 225-236. MR 499785 (80c:13010)
- [5]
- S. Mandall, On efficient generation of ideals, Invent. Math. 75 (1984), 59-67. MR 728138 (85d:13017)
- [6]
- D. G. Northcott and D. Rees, Reductions of ideals in local rings, Proc. Cambridge Philos. Soc. 50 (1954), 147-158. MR 0059889 (15:596a)
- [7]
- A. Sathaye, On the Forster-Eisenbud-Evans conjectures, Invent. Math. 46 (1978), 211-224. MR 499784 (80c:13009)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1986-0857929-2
PII:
S 0002-9939(1986)0857929-2
Article copyright:
© Copyright 1986 American Mathematical Society
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