Gaussian polynomials and content ideals
HTML articles powered by AMS MathViewer
- by William Heinzer and Craig Huneke PDF
- Proc. Amer. Math. Soc. 125 (1997), 739-745 Request permission
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 $f$ of degree $n$ is Gaussian if $c(fg) = c(f)c(g)$ for polynomials $g$ of degree at most $n$.References
- D. D. Anderson and B. G. Kang, Content formulas for polynomials and power series and complete integral closure, J. Algebra 181 (1996), 82–94.
- Winfried Bruns and Jürgen Herzog, Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, vol. 39, Cambridge University Press, Cambridge, 1993. MR 1251956
- S. Glaz and W. Vasconcelos, The content of Gaussian polynomials, J. Algebra, to appear.
- Melvin Hochster, Cyclic purity versus purity in excellent Noetherian rings, Trans. Amer. Math. Soc. 231 (1977), no. 2, 463–488. MR 463152, DOI 10.1090/S0002-9947-1977-0463152-5
- Hideyuki Matsumura, Commutative ring theory, Cambridge Studies in Advanced Mathematics, vol. 8, Cambridge University Press, Cambridge, 1986. Translated from the Japanese by M. Reid. MR 879273
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
- MR Author ID: 89875
- Email: huneke@math.purdue.edu
- Received by editor(s): October 18, 1995
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 1997 American Mathematical Society
- 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