Newbetuts

If $\alpha$ is an algebraic element and $L$ a field, does the polynomial ring $L[\alpha]$ is also a field?

Showing $[\mathbb{Q}(\sqrt[4]{2},\sqrt{3}):\mathbb{Q}]=8$.

Set of elements of degree $2^n$ over a base field is itself a field

Showing $[K(x):K(\frac{x^5}{1+x})]=5$?

Extension of isomorphism of fields

fraction field of the integral closure

In a field extension, if each element's degree is bounded uniformly by $n$, is the extension finite?

On the unicity of splitting field

Generic Element of Compositum of Two Fields [duplicate]

Irreducibility test in a number field

Given a field $\mathbb F$, is there a smallest field $\mathbb G\supseteq\mathbb F$ where every element in $\mathbb G$ has an $n$th root for all $n$?

How is the degree of the minimal polynomial related to the degree of a field extension?

A basis of a field extension contained in a subring

If $[K(\alpha):K]=p\neq q=[K(\beta):K]$ then $[K(\alpha+\beta):K]=pq$

Is $\mathbb{Q}[\sqrt{2},\sqrt{3}]$ the same as $\mathbb{Q}(\sqrt{2},\sqrt{3})$?

Infinite algebraic extension of $\mathbb{Q}$

New posts in extension-field

Prove $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}$ is a simple extension

Algebraic extension of perfect field in which every polynomial has a root is algebraically closed

Separable field extensions without using embeddings or automorphisms

Quadratic Extension of Finite field

If $\alpha$ is an algebraic element and $L$ a field, does the polynomial ring $L[\alpha]$ is also a field?

Showing $[\mathbb{Q}(\sqrt[4]{2},\sqrt{3}):\mathbb{Q}]=8$.

Set of elements of degree $2^n$ over a base field is itself a field

Showing $[K(x):K(\frac{x^5}{1+x})]=5$?

Extension of isomorphism of fields

fraction field of the integral closure

In a field extension, if each element's degree is bounded uniformly by $n$, is the extension finite?

On the unicity of splitting field

Generic Element of Compositum of Two Fields [duplicate]

Irreducibility test in a number field

Given a field $\mathbb F$, is there a smallest field $\mathbb G\supseteq\mathbb F$ where every element in $\mathbb G$ has an $n$th root for all $n$?

How is the degree of the minimal polynomial related to the degree of a field extension?

A basis of a field extension contained in a subring

If $[K(\alpha):K]=p\neq q=[K(\beta):K]$ then $[K(\alpha+\beta):K]=pq$

Is $\mathbb{Q}[\sqrt{2},\sqrt{3}]$ the same as $\mathbb{Q}(\sqrt{2},\sqrt{3})$?

Infinite algebraic extension of $\mathbb{Q}$