New posts in Ring Theory

In the ring $\mathbb{Z}_p$, $p$ is prime, $(a+b)^p=a^p+b^p$ proof?

If $x \in R$ is non-invertible implies $x^2 \in \{\pm x\}$ and $|R| >9$ odd then $R$ is a field

In a commutative ring, GCD exists implies LCM exists?

Does the unit generate the additive group in a unital ring with cyclic additive group?

In a finite commutative ring , every prime ideal is maximal?

Why does one define the polynomial ring $R[x] := R^{(\mathbb N)}$ and not as a subset of functions?

If two zero sets are homeomorphic, is the ring of polynomials over the sets also homeomorphic?

Minimal polynomial of $\alpha + \beta$ over $\mathbb{Q}$

How to show $k[x]$ is not isomorphic to $k[x,y]/(xy+x^3+y^3)$?

Are all non-associative (not necessarily associative) finite division rings finite fields?