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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Gaussian polynomials and content ideals
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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 $n$.
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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
  • 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