The content of a Gaussian polynomial is invertible
Authors:
K. Alan Loper and Moshe Roitman
Journal:
Proc. Amer. Math. Soc. 133 (2005), 12671271
MSC (2000):
Primary 13B25
Published electronically:
December 15, 2004
MathSciNet review:
2111931
Fulltext PDF Free Access
Abstract 
References 
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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 UniversityNewark, Newark, Ohio 43055
Email:
lopera@math.ohiostate.edu
Moshe Roitman
Affiliation:
Department of Mathematics, University of Haifa, Haifa 31905, Israel
Email:
mroitman@math.haifa.ac.il
DOI:
http://dx.doi.org/10.1090/S0002993904078268
PII:
S 00029939(04)078268
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.
