Gaussian polynomials and content ideals

Authors:
William Heinzer and Craig Huneke

Journal:
Proc. Amer. Math. Soc. **125** (1997), 739-745

MSC (1991):
Primary 13A15, 13B25, 13G05, 13H10

DOI:
https://doi.org/10.1090/S0002-9939-97-03921-X

MathSciNet review:
1401742

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that every regular Gaussian polynomial over a locally Noetherian ring has invertible content ideal. We do this by first proving that Gaussian polynomials over an approximately Gorenstein local ring have principal content ideal. We also show over locally Noetherian rings that a regular polynomial of degree is Gaussian if for polynomials of degree at most .

**[AK]**D. D. Anderson and B. G. Kang,*Content formulas for polynomials and power series and complete integral closure*, J. Algebra**181**(1996), 82-94. CMP**96:10****[BH]**W. Bruns and J. Herzog,*Cohen-Macaulay rings*, Cambridge University Press, 1993. MR**95h:13020****[GV]**S. Glaz and W. Vasconcelos,*The content of Gaussian polynomials*, J. Algebra, to appear.**[H]**M. Hochster,*Cyclic purity versus purity in excellent Noetherian rings*, Trans. Amer. Math. Soc.**231**(1977), 463-488. MR**57:3111****[M]**H. Matsumura,*Commutative ring theory*, Cambridge University Press, 1986. MR**88h:13001**

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Additional Information

**William Heinzer**

Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395

Email:
heinzer@math.purdue.edu

**Craig Huneke**

Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395

Email:
huneke@math.purdue.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-03921-X

Received by editor(s):
October 18, 1995

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1997
American Mathematical Society