Newbetuts

How to show that a prime degree separable field extension containing a nontrivial conjugate of a primitive element is Galois and cyclic

closed-form expression for roots of a polynomial

If the Galois group is $S_3$, can the extension be realized as the splitting field of a cubic?

Galois group of $x^4-2$

Is the image of $\Phi_n(x) \in \mathbb{Z}[x]$ in $\mathbb{F}_q[x]$ still a cyclotomic polynomial?

Determine the galois group of $x^5+sx^3+t$

How to show that $\sqrt{2}+\sqrt{3}$ is algebraic?

Galois groups of polynomials and explicit equations for the roots

Algebraic numbers that cannot be expressed using integers and elementary functions

Galois group of irreducible cubic equation

Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$ [duplicate]

Intersection of fixed fields

Is it possible for an irreducible polynomial with rational coefficients to have three zeros in an arithmetic progression?

Why isn't the inverse of the function $x\mapsto x+\sin(x)$ expressible in terms of "the functions one finds on a calculator"?

Contributions of Galois Theory to Mathematics

New posts in galois-theory

Generating Elements of Galois Group

Why does this pattern of "nasty" integrals stop?

Determining a matrix from its characteristic polynomial

Inseparable, irreducible polynomials

Calculating the Galois group of an (irreducible) quintic

How to show that a prime degree separable field extension containing a nontrivial conjugate of a primitive element is Galois and cyclic

closed-form expression for roots of a polynomial

If the Galois group is $S_3$, can the extension be realized as the splitting field of a cubic?

Galois group of $x^4-2$

Is the image of $\Phi_n(x) \in \mathbb{Z}[x]$ in $\mathbb{F}_q[x]$ still a cyclotomic polynomial?

Determine the galois group of $x^5+sx^3+t$

How to show that $\sqrt{2}+\sqrt{3}$ is algebraic?

Galois groups of polynomials and explicit equations for the roots

Algebraic numbers that cannot be expressed using integers and elementary functions

Galois group of irreducible cubic equation

Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$ [duplicate]

Intersection of fixed fields

Is it possible for an irreducible polynomial with rational coefficients to have three zeros in an arithmetic progression?

Why isn't the inverse of the function $x\mapsto x+\sin(x)$ expressible in terms of "the functions one finds on a calculator"?

Contributions of Galois Theory to Mathematics