New posts in ring-theory

Prove that $p$ is prime in $\mathbb{Z}[\sqrt{-3}]$ if and only if $x^2+3$ is irreducible in $\mathbb{F}_p[x]$.

Products of ideals is an ideal and comaximal ideals

For which monic irreducible $f(x)\in \mathbb Z[x]$ , is $f(x^2)$ also irreducible in $\mathbb Z[x]$?

Checking if given polynomials are units in $\mathbb{Z}_7[x]$ [duplicate]

why $\mathbb Z[\sqrt 2] \ncong \mathbb Z[\sqrt 3]$?

Compute the (multiplicative) inverse of $4x+3$ in the field $\frac {\Bbb F_{11}[x]}{\langle x^2+1 \rangle}$?

Prove that $R[x]$ is an integral domain if and only if $R$ is an integral domain. [duplicate]

Importance of the Artin-Wedderburn theorem

The Picard-Brauer short exact sequence

Checking if $\langle 2 \rangle$ is a maximal ideal in $\mathbb{Z}[i]$

Prove that $\mathbb{Q}[\sqrt{2}]=a+b\sqrt{2}$ is isomorphic to $\mathbb{Q}[x]/(x^2-2)$.

Example of finite ring with a non principal ideal

Find all irreducible polynomials of degrees 1,2 and 4 over $\mathbb{F_2}$.

Showing a Functor is not Representable

prove $(n) \supseteq (m)\iff n\mid m\ $ (contains = divides for principal ideals)

Prove that $\Bbb Z[\sqrt{2}, \sqrt{3}]$ does not equal $\Bbb Z[\sqrt{2} + \sqrt{3}]$. [duplicate]

Prove that the augmentation ideal in the group ring $\mathbb{Z}/p\mathbb{Z}G$ is a nilpotent ideal ($p$ is a prime, $G$ is a $p$-group)

Is this ring Noetherian?

When is the map $x\rightarrow x^k$ injective in $\mathbb Z_n$?

On the cubic generalization $(a^3+b^3+c^3+d^3)(e^3+f^3+g^3+h^3 ) = v_1^3+v_2^3+v_3^3+v_4^3$ for the Euler four-square