On the Infinitude of Prime Ideals in Dedekind Domains

2014/03/14 by Velez-Marulanda, Jose A.
#11R04 #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1403.3473

Abstract

Let R be an infinite Dedekind domain with at most finitely many units, and let K denote its field of fractions. We prove the following statement. If L/K is a finite Galois extension of fields and O is the integral closure of R in L, then O contains infinitely many prime ideals. In particular, if O is further a unique factorization domain, then O contains infinitely many non-associate prime elements.

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