Gaussian polynomials and invertibility

Author:
Thomas G. Lucas

Journal:
Proc. Amer. Math. Soc. **133** (2005), 1881-1886

MSC (2000):
Primary 13A15, 13B25

DOI:
https://doi.org/10.1090/S0002-9939-05-07977-3

Published electronically:
February 24, 2005

MathSciNet review:
2137851

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The content of a polynomial over a commutative ring is the ideal of generated by the coefficients of . If for each polynomial , then is said to be Gaussian. If is an invertible ideal of , then is Gaussian. An open question has been whether the converse holds for a polynomial whose content is a regular ideal of . The main theorem shows slightly more than this; namely, if has no nonzero annihilators, then .

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Additional Information

**Thomas G. Lucas**

Affiliation:
Department of Mathematics and Statistics, University of North Carolina Charlotte, Charlotte, North Carolina 28223

Email:
tglucas@uncc.edu

DOI:
https://doi.org/10.1090/S0002-9939-05-07977-3

Keywords:
Gaussian polynomial,
content,
$Q_0$-invertible

Received by editor(s):
November 3, 2003

Published electronically:
February 24, 2005

Communicated by:
Bernd Ulrich

Article copyright:
© Copyright 2005
American Mathematical Society

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