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Is $x \in X$ isolated iff the ideal $M_x := \{f \in C(X, \mathbb R) :f(x)=0\}$ of $C(X, \mathbb R)$ is principal ?

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List Question

Trying to prove $Z(I(A))=\bar A$

Pull back image of maximal ideal under surjective ring homomorphism is maximal

Grobner basis and subsets

Is this homomorphism in general surjective?

$I^{j}/I^{j+1} \cong R/I$ for any ideal I in ring R.

Polynomial ideals

A question concerning to show that $V(I)$ is open if $I$ is radical ideal

Sum of ideals in polynomial rings

Norm of an ideal is finite

Finding powers of prime ideals from its generators and understanding generator notation

If $(X,d)$ is a finite metric space , then is every prime ideal of $C(X, \mathbb R)$ maximal?

Is $x \in X$ isolated iff the ideal $M_x := \{f \in C(X, \mathbb R) :f(x)=0\}$ of $C(X, \mathbb R)$ is principal ?

What is a linear combination, exactly?

Proving an ideal is maximal

A and B left ideals of ring R. Is $BA⊆A$?

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