A Dirichlet Theorem for Polynomial Rings
نویسنده
چکیده
We prove a Dirichlet theorem for polynomial rings: Let F be a pseudo algebraically closed field (i.e., each nonempty variety defined over F has an F-rational point). Then for all relatively prime polynomials a(X), b(X) ∈ F [X] and for every sufficiently large integer n there exist infinitely many polynomials c(X) ∈ F [X] such that a(X) + b(X)c(X) is irreducible of degree n, provided that F has a separable extension of degree n.
منابع مشابه
Ja n 20 07 DIRICHLET ’ S THEOREM FOR POLYNOMIAL RINGS
We prove Dirichlet's theorem for polynomial rings: Let F be a pseudo algebraically closed field. Then for all relatively prime polynomials a(X), b(X) ∈ F [X] and for every sufficiently large integer n there exist infinitely many polynomials c(X) ∈ F [X] such that a(X) + b(X)c(X) is irreducible of degree n, provided that F has a separable extension of degree n.
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