Newbetuts

Is a field perfect iff the primitive element theorem holds for all extensions, and what about function fields

Is it possible to have a vector space in which $\vec{v}=-\vec{v}$, yet $\vec{v}\neq \vec{0}$?

Prove that $[\mathbb{Q}(\sqrt[r]{p_1},\cdots ,\sqrt[r]{p_n}):\mathbb{Q}]=r^n$

Examples of fields which are not perfect

What is a maximal abelian extension of a number field and what does its Galois group look like?

Proving the universal mapping property for polynomial rings

Proof that every field is perfect?

Is it possible to construct an ordered field which is also algebraically closed?

Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?

Fraction field of $F[X,Y](f)$ isomorphic to $F(X)[Y]/(f)$

Product of degree of two field extensions of prime degree

Minimal polynomial of $1 + 2^{1/3} + 4^{1/3}$

Extension fields isomorphic to fields of matrices

A curiosity: how do we prove $\mathbb{R}$ is closed under addition and multiplication?

How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$ [duplicate]

New posts in field-theory

Determine the degree of the extension $\mathbb{Q}(\sqrt{3 + 2\sqrt{2}})$.

The kernel of the unique homomorphism $\varphi:\mathbb Z\to K$ is a prime ideal.

Using rings with unity vs without unity in an algebra course

What's the difference between hyperreal and surreal numbers?

How do I prove $F(a)=F(a^2)?$

Is a field perfect iff the primitive element theorem holds for all extensions, and what about function fields

Is it possible to have a vector space in which $\vec{v}=-\vec{v}$, yet $\vec{v}\neq \vec{0}$?

Prove that $[\mathbb{Q}(\sqrt[r]{p_1},\cdots ,\sqrt[r]{p_n}):\mathbb{Q}]=r^n$

Examples of fields which are not perfect

What is a maximal abelian extension of a number field and what does its Galois group look like?

Proving the universal mapping property for polynomial rings

Proof that every field is perfect?

Is it possible to construct an ordered field which is also algebraically closed?

Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?

Fraction field of $F[X,Y](f)$ isomorphic to $F(X)[Y]/(f)$

Product of degree of two field extensions of prime degree

Minimal polynomial of $1 + 2^{1/3} + 4^{1/3}$

Extension fields isomorphic to fields of matrices

A curiosity: how do we prove $\mathbb{R}$ is closed under addition and multiplication?

How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$ [duplicate]