Give $3$ examples of a field extensions which are neither normal nor separable.
67157
Example of an non-normal inseparable field extension
98256
Subfields of $\mathbb{Q}(\sqrt{2},\sqrt{3})$
7010
Example of two non-isomorphic fields which embed inside each other
151978
Splitting field of x^3-2 as a simple extension
35401
Examples of finite groups that are not a semidirect product
18003
Standard example where Jacobson radical not equal nilradical
93358
Find an example of a non-surjective field endomorphism
147158
Galois group of a non-separable polynomial
79450
For field extensions $F\subsetneq K \subset F(x)$, $x$ is algebraic over $K$
142707
Intermediate fields of a finite field extension that is not separable
158924
Example of composition of two normal field extensions which is not normal.
116628
Example of Galois extension whose Galois group is $A_4$
147069
Intersection of field extensions
136592
Examples of manifolds that are not boundaries
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
150961
An example for a homomorphism that is not an automorphism
104634
Galois extension is (not) transitive