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Register a new userOn the Infinitude of Prime Ideals in Dedekind Domains
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Jose A. Velez-Marulanda
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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 $mathcal{O}$ is the integral closure of $R$ in $L$, then $mathcal{O}$ contains infinitely many prime ideals. In particular, if $mathcal{O}$ is further a unique factorization domain, then $mathcal{O}$ contains infinitely many non-associate prime elements.
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We study the R-torsionfree part of the Ziegler spectrum of an order Lambda over a Dedekind domain R. We underline and comment on the role of lattices over Lambda. We describe the torsionfree part of the spectrum when Lambda is of finite lattice representation type.
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