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New posts in abstract-algebra
T[x] Euclidean if and only if T is a field. [duplicate]
abstract-algebra
How to I prove this fact about two sided ideals?
abstract-algebra
ideals
Prove that the polynomial $x^5+2x+1$ is irreducible over $\mathbb{Z}$.
abstract-algebra
polynomials
irreducible-polynomials
Finding the ring of integers of $\mathbb Q[\alpha]$ with $\alpha^5=2\alpha+2$.
abstract-algebra
algebraic-number-theory
integer-rings
Necklace problem with Burnside's lemma
abstract-algebra
group-theory
Writing a vector space as a direct product of T-irreducible subspaces
linear-algebra
abstract-algebra
vector-spaces
representation-theory
A binary operation defined on a set with one element
abstract-algebra
solution-verification
Find kernel of induced map after tensoring
abstract-algebra
modules
tensor-products
Formal power series with coefficient in $\{0,1 \}$ which is not rational
abstract-algebra
power-series
$F[x]/(x^2)\cong F[x]/(x^2 - 1)$ if and only if F has characteristic 2
abstract-algebra
ring-theory
field-theory
Cyclotomic polynomials explicitly solvable??
abstract-algebra
polynomials
Character table of the non-abelian group of order 21
abstract-algebra
group-theory
representation-theory
If $L\mid K$ is a finite extension of fields then K is perfect iff L is perfect
abstract-algebra
algebraic-geometry
field-theory
extension-field
If a normal $K/F$ has no intermediate extensions, then $[K : F]$ is prime
abstract-algebra
field-theory
galois-theory
Structure theorem of finite rings
abstract-algebra
ring-theory
finite-rings
Aut(GxH) isomorphic to Aut(G)xAut(H)
abstract-algebra
"Natural" categories where monomorphisms differ from injective morphisms
abstract-algebra
category-theory
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 $G$.
abstract-algebra
group-theory
How to show fraction field is flat (without localization)
abstract-algebra
ring-theory
modules
homological-algebra
Why is the extension $k(x,\sqrt{1-x^2})/k$ purely transcendental?
abstract-algebra
algebraic-geometry
field-theory
extension-field
algebraic-curves
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