Newbetuts

What's the rationale for requiring that a field be a $\boldsymbol{non}$-$\boldsymbol{trivial}$ ring?

In plain language, what's the significance of a field?

What is Abstract Algebra essentially?

Why is this isomorphism $M \otimes_K L \stackrel{\simeq}{\longrightarrow} M^{[L:K]}$ an isomorphism of $M$ - algebras?

Equal simple field extensions?

What's so special about characteristic 2?

Unique quadratic subfield of $\mathbb{Q}(\zeta_p)$ is $\mathbb{Q}(\sqrt{p})$ if $p \equiv 1$ $(4)$, and $\mathbb{Q}(\sqrt{-p})$ if $p \equiv 3$ $(4)$

Order of field extension

Intuitive reasoning why are quintics unsolvable

Representing a countable field by $\Bbb N$ [transport of algebraic structure]

Why is the Galois Correspondence intuitively plausible?

What kind of work do modern day algebraists do?

Is there a purely algebraic proof of the Fundamental Theorem of Algebra?

What is difference between a ring and a field?

New posts in field-theory

Proof of Existence of Algebraic Closure: Too simple to be true?

Galois Field GF(4)

Algebraic closure for $\mathbb{Q}$ or $\mathbb{F}_p$ without Choice?

Why is the category of fields seemingly so poorly behaved?

Existence of irreducible polynomials over finite field

Do finite algebraically closed fields exist?

What's the rationale for requiring that a field be a $\boldsymbol{non}$-$\boldsymbol{trivial}$ ring?

In plain language, what's the significance of a field?

What is Abstract Algebra essentially?

Why is this isomorphism $M \otimes_K L \stackrel{\simeq}{\longrightarrow} M^{[L:K]}$ an isomorphism of $M$ - algebras?

Equal simple field extensions?

What's so special about characteristic 2?

Unique quadratic subfield of $\mathbb{Q}(\zeta_p)$ is $\mathbb{Q}(\sqrt{p})$ if $p \equiv 1$ $(4)$, and $\mathbb{Q}(\sqrt{-p})$ if $p \equiv 3$ $(4)$

Order of field extension

Intuitive reasoning why are quintics unsolvable

Representing a countable field by $\Bbb N$ [transport of algebraic structure]

Why is the Galois Correspondence intuitively plausible?

What kind of work do modern day algebraists do?

Is there a purely algebraic proof of the Fundamental Theorem of Algebra?

What is difference between a ring and a field?