2 февр. 2024 г. · I am taking undergrad level field theory and I am doing a problem: Suppose K[x] is a polynomial ring over the field K and F is a subfield of K.

10 апр. 2011 г. · EDIT: A perfect field is defined as follows: Any field of characteristic 0 is perfect, and a field of characteristic p is said to be perfect if ...

6 окт. 2011 г. · One of the common definitions is that a field is perfect iff every algebraic extension field is separable. In this case half of what you want is ...

6 июн. 2015 г. · We say that F is perfect if every polynomial f(x)∈F[x] is separable, where we say that f(x) is separable if its irreducible factors have no ...

23 июл. 2017 г. · Let f(x)=xp−a. We prove that f is irreducible and inseparable. If α is a root of xp−a, then xp−a=(x−α)p, so α is a multiple root of f (with ...

19 апр. 2023 г. · I have a question about the the proof of the above. The two are both about proving that a field F whose characteristic is p(prime) is perfect ...

2 мар. 2019 г. · Definition 1: Let k be a field. It is called perfect field, if char k=0 or char k=p with kp=k.

17 янв. 2021 г. · A field is said to be perfect if it has no non-separable algebraic extensions. Aside from being very useful as ground fields, they have a nice ...

19 июл. 2019 г. · Suppose E/K is a field extension and p∈K[x] is irreducible (in K[x]). Then every root of p in E is simple.

7 февр. 2012 г. · We know that all finite fields are perfect (fields with char p). Also fields with char 0 (infinite fields) are perfect. Then what are the fields that are not ...