New posts in Ring Theory

Recognizing Principal Ideals

Do both versions (invariant and primary) of the Fundamental Theorem for Finitely Generated Abelian Groups hold at the same time?

$x^n = x$ implies commutativity, a universal algebraic proof?

Is $\mathbb{Z}[\sqrt{29}] $ a PID

Problem in the "proof" of Eisenstein's criterion on irreducibility.

Quotient ring being isomorphic to the initial ring

A non-zero ring $R$ is a field if and only if for any non-zero ring $S$, any ring homomorphism from $R$ to $S$ is injective.

Finding all the maximal ideals of $C([0,1])$ and also prime ideals in it which are not maximal

Is $\langle x^2+1,y\rangle$ maximal or prime in $\Bbb{R}[x,y]$ or $\Bbb{C}[x,y]$

Why is it that if a ring is simple, its center must be a field?