7 июн. 2010 г. · Perfect fields are fields all of whose algebraic extensions are separable, so their algebraic and separable closure coincide. Finite fields are ...

28 июл. 2018 г. · If K/k is a finite normal extension of fields, is there always an intermediate field F such that F/k is purely inseparable and K/F is separable?

23 мая 2024 г. · I am wondering if it is always possible to take the Berkovich completion after the algebraic closure of a field, to the effect that one does ...

12 янв. 2014 г. · where Xy=X×YSpeck(y) is the fiber over y and in some book they take K as the algebraic closure but in other books as the separable closure.

11 февр. 2010 г. · Can the algebraic closure of a complete field be complete and of infinite degree? ... Yes, this is yet another "foundational" question in ...

1 нояб. 2009 г. · Saying an irreducible polynomial f(x) is inseparable is the same as saying that f(x) ramifies when we extend Q[x] to L[x], where L is the splitting field of f( ...

16 авг. 2016 г. · The completion of the algebraic closure of a valued field is algebraically closed and complete. So any further operation of closure or completion gives you a ...

28 окт. 2009 г. · c) Every x∈K is separable, i.e. the minimum polynomial of x over k is separable. [Which means that its roots are distinct in an algebraic ...

27 мая 2011 г. · An arbitrary algebraic extension F⊂K may not possess an intermediate extension E that is purely inseparable over F and over which K is separable.

18 февр. 2014 г. · The characterization of when a finite extension (separable or not) admits finitely many intermediate fields is exactly that it is a primitive extension.