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The content of a Gaussian polynomial is invertible |
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| Authors: | K. Alan Loper Moshe Roitman |
| Affiliation: | Department of Mathematics, Ohio State University-Newark, Newark, Ohio 43055 ; Department of Mathematics, University of Haifa, Haifa 31905, Israel |
| Abstract: | Let  be an integral domain and let  be a nonzero polynomial in ![$R[X]$](http://www.ams.org/proc/2005-133-05/S0002-9939-04-07826-8/gif-abstract0/img3.gif){kind=small} . The content of  is the ideal  generated by the coefficients of  . The polynomial  is called Gaussian if  for all ![$g(X) in R[X]$](http://www.ams.org/proc/2005-133-05/S0002-9939-04-07826-8/gif-abstract0/img9.gif){kind=small} . It is well known that if  is an invertible ideal, then  is Gaussian. In this note we prove the converse. |
| Keywords: | Content Gaussian polynomial invertible ideal locally principal prestable ideal |
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