Square-free criteria for polynomials using no derivatives
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- by E. Alkan, A. I. Bonciocat, N. C. Bonciocat and A. Zaharescu PDF
- Proc. Amer. Math. Soc. 135 (2007), 677-687 Request permission
Abstract:
We provide some square-free criteria for primitive polynomials over unique factorization domains, which do not make use of derivatives or discriminants. Using some ideas of Ostrowski we establish nonvanishing conditions for determinants of matrices with polynomial entries and deduce square-free criteria for polynomials in several variables.References
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Additional Information
- E. Alkan
- Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Altgeld Hall, 1409 W. Green Street, Urbana, Illinois 61801
- Email: alkan@math.uiuc.edu
- A. I. Bonciocat
- Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 014700, Romania
- Email: Anca.Bonciocat@imar.ro
- N. C. Bonciocat
- Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 014700, Romania
- Email: Nicolae.Bonciocat@imar.ro
- A. Zaharescu
- Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Altgeld Hall, 1409 W. Green Street, Urbana, Illinois 61801
- MR Author ID: 186235
- Email: zaharesc@math.uiuc.edu
- Received by editor(s): September 12, 2005
- Received by editor(s) in revised form: October 10, 2005
- Published electronically: September 11, 2006
- Additional Notes: This research was partially supported by the CERES Programs 4-147 and 4-187/2004 of the Romanian Ministry of Education and Research.
- Communicated by: Ken Ono
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 677-687
- MSC (2000): Primary 11C08, 11C20
- DOI: https://doi.org/10.1090/S0002-9939-06-08526-1
- MathSciNet review: 2262863