Dirichlet’s theorem for polynomial rings
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- by Lior Bary-Soroker PDF
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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 $a(X), b(X)\in F[X]$ and for every sufficiently large integer $n$ there exist infinitely many polynomials $c(X)\in F[X]$ such that $a(X) + b(X)c(X)$ is irreducible of degree $n$, provided that $F$ has a separable extension of degree $n$.References
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Additional Information
- Lior Bary-Soroker
- Affiliation: School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978 Israel
- Address at time of publication: Department of Mathematics, The Hebrew University, Givat Ram, Jerusalem 91904, Israel
- MR Author ID: 797213
- ORCID: 0000-0002-1303-247X
- Email: barylior@post.tau.ac.il
- Received by editor(s): January 29, 2007
- Received by editor(s) in revised form: July 23, 2007, September 11, 2007, and January 2, 2008
- Published electronically: August 13, 2008
- Communicated by: Ted Chinburg
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 73-83
- MSC (2000): Primary 12E30, 12E25
- DOI: https://doi.org/10.1090/S0002-9939-08-09474-4
- MathSciNet review: 2439427