Dirichlet’s theorem for polynomial rings

DOI10.1090/S0002-9939-08-09474-4zbMath1259.12002arXivmath/0612801MaRDI QIDQ3600585

Lior Bary-Soroker

Publication date: 5 February 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612801

zbMATH Keywords

arithmetic progressionDirichlet's theoremHilbert's irreducibility theoremPAC fieldfield arithmetics

Mathematics Subject Classification ID

Hilbertian fields; Hilbert's irreducibility theorem (12E25) Field arithmetic (12E30)

Related Items (12)

A NOTE ON DENSITY AND THE DIRICHLET CONDITION ⋮ On bounded elementary generation for \(\mathrm{SL}_n\) over polynomial rings ⋮ The Golomb topology of polynomial rings, II ⋮ Irreducible values of polynomials ⋮ The Schinzel hypothesis for polynomials ⋮ Irreducibility and embedding problems ⋮ Prime polynomials in short intervals and in arithmetic progressions ⋮ On PAC extensions and scaled trace forms ⋮ On pseudo algebraically closed extensions of fields ⋮ The Golomb Topology of Polynomial Rings ⋮ Specialization results in Galois theory ⋮ On the Galois theory of generalized Laguerre polynomials and trimmed exponential

Cites Work

• Galois stratification over Frobenius fields
• PAC fields over finitely generated fields
• The embedding problem over a Hilbertian PAC-field
• Pseudo algebraically closed fields over rings
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