Abstract
We investigate the following question. Let K be a global field, i.e. a number field or an algebraic function field of one variable over a finite field of constants. Let W K be a set of primes of K, possibly infinite, such that in some fixed finite separable extension L of K, all the primes of W K do not have factors of relative degree 1. Let M be a finite extension of K and let W M be the set of all the M-primes above the primes of W K . Then does W M have the same property? The answer is “always” for one variable algebraic function fields over finite fields of constants and “not always” for number fields. In this paper we give a complete description of the conditions under which W M inherits and does not inherit the above described property.
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