Newbetuts

Let $R$ be a commutative domain with field of fractions $F$. Prove that $F$ is an injective $R$-module.

The ring $\mathbb{C}[x,y]/\langle xy \rangle$

The center of a group is an abelian subgroup

Show that $(2+i)$ is a prime ideal

Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$

Embed finite field in algebraic closed field

How to prove $X^{4}+X^{3}+X^{2}+X+1$ is irreductible in $\mathbb{F}_{2}$

Exhibit the ideals of $\mathbb{Z}[x]/(2,x^3+1)$

Gorenstein dimension vs projective dimension

In a metric Lie algebra, is the orthogonal complement of a Lie subalgebra a Lie subalgebra?

Determine all homomorphic images of $D_4$ up to isomorphism.

How many homomorphism from $S_3$ to $S_4$?

Does this theorem/collection of theorems have a name? Or is it just seen as obvious?

Exercises to help a student become accustomed to Sweedler notation

New posts in abstract-algebra

Principal ideal domain not euclidean

If $G$ is a group, show that $x^2ax=a^{-1}$ has a solution if and only if $a$ is a cube in $G$

How to prove the tensor product of two copies of $\mathbb{H}$ is isomorphic to $M_4 (\mathbb{R})$?

Pair notation in multivariate polynomial rings: ideal vs. tuple

Algebras that are free modules over a subalgebra

Show that a group of order $p^2q^2$ is solvable

Let $R$ be a commutative domain with field of fractions $F$. Prove that $F$ is an injective $R$-module.

The ring $\mathbb{C}[x,y]/\langle xy \rangle$

The center of a group is an abelian subgroup

Show that $(2+i)$ is a prime ideal

Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$

Embed finite field in algebraic closed field

How to prove $X^{4}+X^{3}+X^{2}+X+1$ is irreductible in $\mathbb{F}_{2}$

Exhibit the ideals of $\mathbb{Z}[x]/(2,x^3+1)$

Gorenstein dimension vs projective dimension

In a metric Lie algebra, is the orthogonal complement of a Lie subalgebra a Lie subalgebra?

Determine all homomorphic images of $D_4$ up to isomorphism.

How many homomorphism from $S_3$ to $S_4$?

Does this theorem/collection of theorems have a name? Or is it just seen as obvious?

Exercises to help a student become accustomed to Sweedler notation