Factorization of Prime Ideals Sample Clauses

Factorization of Prime Ideals. Now consider the situation where we have a finite extension, L, of a number field K. The ring of integers in K, denoted OK, is a Dedekind domain. Given a prime ideal ℘ ⊂ OK, we know that ℘OL is an ideal contained in OL. Since OL is also a Dedekind domain, ℘OL = Y Pei where Pi are prime ideals contained in OL.
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