New posts in Maximal And Prime Ideals

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 $\Bbb{C}[x,y]$

If $ U$ is maximal among non-principal ideals show that $U$ is prime. (Hints?)

Counter-example: If $J$ is prime then $f^{-1} (J) $ is prime. $f$ need not be unital.

$\mathfrak p$ be a prime ideal of a commutative ring $R$ , then $R_\mathfrak p/\mathfrak pR_\mathfrak p$ is the field of fractions of $R/\mathfrak p$?

Local ring with finite maximal ideal is finite

Can a non-local ring have only two prime ideals?

How do ring homomorphism R → ℤ correspond to prime ideals of R?

Radical of an ideal equals the intersection of all prime ideals containing it.

What's so special about a prime ideal?