Square-free criteria for polynomials using no derivatives

Alkan, E.; Bonciocat, A.; Bonciocat, N.; Zaharescu, A.

doi:10.1090/S0002-9939-06-08526-1

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.

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