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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Square-free criteria for polynomials using no derivatives


Authors: E. Alkan, A. I. Bonciocat, N. C. Bonciocat and A. Zaharescu
Journal: Proc. Amer. Math. Soc. 135 (2007), 677-687
MSC (2000): Primary 11C08, 11C20
Published electronically: September 11, 2006
MathSciNet review: 2262863
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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.


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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
Email: zaharesc@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08526-1
PII: S 0002-9939(06)08526-1
Keywords: Square-free criteria, primitive polynomials, resultants, Frobenius map.
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
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.