Dirichlet's theorem for polynomial rings

Research output: Contribution to journalArticlepeer-review

Abstract

We prove the following form of Dirichlet's theorem for polynomial rings in one indeterminate over a pseudo algebraically closed field F. 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.

Original languageEnglish
Pages (from-to)73-83
Number of pages11
JournalProceedings of the American Mathematical Society
Volume137
Issue number1
DOIs
StatePublished - Jan 2009

Keywords

  • Arithmetic progression
  • Dirichlet's theorem
  • Field arithmetics
  • Hilbert's irreducibility theorem
  • PAC field

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