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A generalized Dedekind-Mertens lemma and its converse
Author(s):
Alberto
Corso;
William
Heinzer;
Craig
Huneke
Journal:
Trans. Amer. Math. Soc.
350
(1998),
5095-5109.
MSC (1991):
Primary 13A15;
Secondary 13B25, 13G05, 13H10
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Abstract:
We study content ideals of polynomials and their behavior under multiplication. We give a generalization of the Lemma of Dedekind-Mertens and prove the converse under suitable dimensionality restrictions.
References:
- [AG]
- Arnold, J., Gilmer, R., On the contents of polynomials, Proc. Amer. Math. Soc. 24 (1970), 556-562. MR 40:5581
- [AK]
- Anderson, D.D., Kang, B.G., Content formulas for polynomials and power series and complete integral closure, J. Algebra 181 (1996), 82-94. MR 97c:13014
- [BG]
- Bruns, W., Guerrieri, A., The Dedekind-Mertens formula and determinantal rings, to appear, Proc. Amer. Math. Soc. CMP 97:17
- [BH]
- W. Bruns, W., Herzog, J., Cohen-Macaulay Rings, Cambridge University Press, Cambridge, 1993. MR 95h:13020
- [CVV]
- Corso, A., Vasconcelos, W.V, Villarreal, R., Generic Gaussian ideals, J. Pure Appl. Algebra 125 (1998), 117-127. CMP 98:07
- [E]
- Edwards, H., Divisor Theory, Birkhäuser, Boston, 1990. MR 93h:11115
- [GGP]
- Gilmer, R., Grams, A., Parker, T., Zero divisors in power series rings, J. Reine Angew. Math. 278/279 (1975), 145-164. MR 52:8117
- [GV]
- Glaz, S., Vasconcelos, W.V., The content of Gaussian polynomials, to appear, J. Algebra.
- [HH1]
- Heinzer, W., Huneke, C., Gaussian polynomials and content ideals, Proc. Amer. Math. Soc. 125 (1997), 739-745. MR 97e:13015
- [HH2]
- Heinzer, W., Huneke, C., The Dedekind-Mertens lemma and the contents of polynomials, Proc. Amer. Math. Soc. 126 (1998), 1305-1309. CMP 97:05
- [Ho]
- Hochster, M., Cyclic purity versus purity in excellent Noetherian rings, Trans. Amer. Math. Soc. 231 (1977), 463-488. MR 57:3111
- [Mat]
- Matsumura, H., Commutative Ring Theory, Cambridge University Press, Cambridge, 1986. MR 88h:13001
- [N]
- Northcott, D.G., A generalization of a theorem on the content of polynomials, Proc. Camb. Philos. Soc. 55 (1959), 282-288. MR 22:1600
- [Re1]
- Rees, D., A note on analytically unramified local rings, J. London Math. Soc. 36 (1961), 24-28. MR 23:A3761
- [Re2]
- Rees, D., A note on asymptotically unmixed ideals, Math. Proc. Camb. Phil. Soc. 98 (1985), 33-35. MR 86k:13015
- [ZS]
- Zariski, O., Samuel, P., Commutative Algebra, vol. II, Springer, Berlin, 1975. MR 52:10706
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Additional Information:
Alberto
Corso
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47906
Address at time of publication:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email:
corso@math.msu.edu
William
Heinzer
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47906
Email:
heinzer@math.purdue.edu
Craig
Huneke
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47906
Email:
huneke@math.purdue.edu
DOI:
10.1090/S0002-9947-98-02176-X
PII:
S 0002-9947(98)02176-X
Keywords:
Content ideal of a polynomial,
integral closure of an ideal,
Dedekind--Mertens Lemma,
Dedekind--Mertens number
Received by editor(s):
February 10, 1997
Additional Notes:
The authors gratefully acknowledge partial support from the NSF
Dedicated:
To Wolmer V. Vasconcelos on the occasion of his sixtieth birthday
Copyright of article:
Copyright
1998,
American Mathematical Society
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