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Is there a field extension over the real numbers that is not the same as the field of complex numbers?

Can we always find a primitive element that is a square?

General way to determine $\mathbb{Q}(\gamma) = \mathbb{Q}(\alpha,\beta)$ given $\alpha$ and $\beta$

Transitivity of the discriminant of number fields

For $L/K$, is $\mathcal{O}_L$ the integral closure of $\mathcal{O}_K$

Field extensions of finite degree and primitive elements

Which cyclotomic fields are different?

Can we extend the real numbers by using hexagonal coordinates on a plane?

A finite field extension of $\mathbb R$ is either $\mathbb R$ or isomorphic to $\mathbb C$

Is it possible to construct a field larger than the complex numbers?

The real numbers are a field extension of the rationals?

Given a proper field extension $L/K$, can we have $L\cong K$? [duplicate]

galois group of finite field [duplicate]

What is the degree of a real closure of an ordered field?

Determine the degree of the splitting field for $f(x)=x^{15}-1$.

New posts in extension-field

Elements of $\mathbb Q(2^{1/3})$

Proof that a finite separable extension has only finite many intermediate fields

Separability and tensor product of fields

degree of a field extension

Geometric interpretation of different types of field extensions?

Is there a field extension over the real numbers that is not the same as the field of complex numbers?

Can we always find a primitive element that is a square?

General way to determine $\mathbb{Q}(\gamma) = \mathbb{Q}(\alpha,\beta)$ given $\alpha$ and $\beta$

Transitivity of the discriminant of number fields

For $L/K$, is $\mathcal{O}_L$ the integral closure of $\mathcal{O}_K$

Field extensions of finite degree and primitive elements

Which cyclotomic fields are different?

Can we extend the real numbers by using hexagonal coordinates on a plane?

A finite field extension of $\mathbb R$ is either $\mathbb R$ or isomorphic to $\mathbb C$

Is it possible to construct a field larger than the complex numbers?

The real numbers are a field extension of the rationals?

Given a proper field extension $L/K$, can we have $L\cong K$? [duplicate]

galois group of finite field [duplicate]

What is the degree of a real closure of an ordered field?

Determine the degree of the splitting field for $f(x)=x^{15}-1$.