The content of a Gaussian polynomial is invertible

Authors:
K. Alan Loper and Moshe Roitman

Journal:
Proc. Amer. Math. Soc. **133** (2005), 1267-1271

MSC (2000):
Primary 13B25

DOI:
https://doi.org/10.1090/S0002-9939-04-07826-8

Published electronically:
December 15, 2004

MathSciNet review:
2111931

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be an integral domain and let be a nonzero polynomial in . The content of is the ideal generated by the coefficients of . The polynomial is called Gaussian if for all . It is well known that if is an invertible ideal, then is Gaussian. In this note we prove the converse.

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Additional Information

**K. Alan Loper**

Affiliation:
Department of Mathematics, Ohio State University-Newark, Newark, Ohio 43055

Email:
lopera@math.ohio-state.edu

**Moshe Roitman**

Affiliation:
Department of Mathematics, University of Haifa, Haifa 31905, Israel

Email:
mroitman@math.haifa.ac.il

DOI:
https://doi.org/10.1090/S0002-9939-04-07826-8

Keywords:
Content,
Gaussian polynomial,
invertible ideal,
locally principal,
prestable ideal

Received by editor(s):
September 16, 2003

Published electronically:
December 15, 2004

Additional Notes:
The second author thanks the Mathematics Department of Ohio State University for its hospitality

Communicated by:
Bernd Ulrich

Article copyright:
© Copyright 2004
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.