New posts in abstract-algebra

T[x] Euclidean if and only if T is a field. [duplicate]

How to I prove this fact about two sided ideals?

Prove that the polynomial $x^5+2x+1$ is irreducible over $\mathbb{Z}$.

Finding the ring of integers of $\mathbb Q[\alpha]$ with $\alpha^5=2\alpha+2$.

Necklace problem with Burnside's lemma

Writing a vector space as a direct product of T-irreducible subspaces

A binary operation defined on a set with one element

Find kernel of induced map after tensoring

Formal power series with coefficient in $\{0,1 \}$ which is not rational

$F[x]/(x^2)\cong F[x]/(x^2 - 1)$ if and only if F has characteristic 2

Cyclotomic polynomials explicitly solvable??

Character table of the non-abelian group of order 21

If $L\mid K$ is a finite extension of fields then K is perfect iff L is perfect

If a normal $K/F$ has no intermediate extensions, then $[K : F]$ is prime

Structure theorem of finite rings

Aut(GxH) isomorphic to Aut(G)xAut(H)

"Natural" categories where monomorphisms differ from injective morphisms

If a normal subgroup $N$ of order $p$($p$ prime) is contained in a group $G$ of order $p^n$,then $N$ is in the center of $G$.

How to show fraction field is flat (without localization)

Why is the extension $k(x,\sqrt{1-x^2})/k$ purely transcendental?