Newbetuts

$(\mathbb R, \oplus)$ is a group. Define a multiplication with which we get a field. Where $a \oplus b = a + b +1$

What is the meaning of $\mathbf{Q}(\sqrt{2},\sqrt{3})$

What is the meaning of "algebraically indistinguishable"

Show $\mathbb{Q}( \sqrt{5},\sqrt{7} ) = \mathbb{Q}( \sqrt{5} + \sqrt{7} )$

Field extensions, inverse limits, notation and roots of unity

Multiplicative nature of the separability degree

Find inverse of element in a binary field

Prove $-(-a)=a$ using only ordered field axioms

Can Hilbert spaces be defined over fields other than $\mathbb R$ and $\mathbb C$?

Is $K(X)$ never algebraically closed?

Minimal polynomial of intermediate extensions under Galois extensions.

If $K$ is algebraically closed, is the fixed field of an involution real-closed?

Show that $9+9x+3x^3+6x^4+3x^5+x^6$ is irreducible given one of its roots

An example for a homomorphism that is not an automorphism

Splitting field of $x^n-a$ contains all $n$ roots of unity

Is there a field extension $K / \Bbb Q$ such that $\text{Aut}_{\Bbb Q}(K) \cong \Bbb Z$?

Is an infinite field always isomorphic to a non-trivial fraction field?

New posts in field-theory

Closure of a number field with respect to roots of a cubic

What is the Cardinality of this set? [closed]

Find the minimal polynomial for $\sqrt[3]{2} + \sqrt[3]{4}$ over $\mathbb{Q}$

$(\mathbb R, \oplus)$ is a group. Define a multiplication with which we get a field. Where $a \oplus b = a + b +1$

What is the meaning of $\mathbf{Q}(\sqrt{2},\sqrt{3})$

What is the meaning of "algebraically indistinguishable"

Show $\mathbb{Q}( \sqrt{5},\sqrt{7} ) = \mathbb{Q}( \sqrt{5} + \sqrt{7} )$

Field extensions, inverse limits, notation and roots of unity

Multiplicative nature of the separability degree

Find inverse of element in a binary field

Prove $-(-a)=a$ using only ordered field axioms

Can Hilbert spaces be defined over fields other than $\mathbb R$ and $\mathbb C$?

Is $K(X)$ never algebraically closed?

Minimal polynomial of intermediate extensions under Galois extensions.

If $K$ is algebraically closed, is the fixed field of an involution real-closed?

Show that $9+9x+3x^3+6x^4+3x^5+x^6$ is irreducible given one of its roots

An example for a homomorphism that is not an automorphism

Splitting field of $x^n-a$ contains all $n$ roots of unity

Is there a field extension $K / \Bbb Q$ such that $\text{Aut}_{\Bbb Q}(K) \cong \Bbb Z$?

Is an infinite field always isomorphic to a non-trivial fraction field?