Irreducibility criteria for compositions of multivariate polynomials |
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Authors: | N C Bonciocat |
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Institution: | 1.Simion Stoilow Institute of Mathematics of the Romanian Academy,Bucharest,Romania |
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Abstract: | We provide irreducibility criteria for compositions of multivariate polynomials over a field K, of the form \({f(X_{1},\ldots ,X_{r-1},g(X_{1},\ldots ,X_{r}))}\), with \({f,g\in KX_{1},\ldots ,X_{r}]}\), for the case that \({f}\) as a polynomial in Xr is irreducible over \({K(X_{1},\ldots ,X_{r-1})}\) and has leading coefficient divisible by a power of an irreducible polynomial \({p(X_{1},\ldots ,X_{r-1})}\) of sufficiently large degree with respect to \({X_{r-1}}\). |
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