Newbetuts

Show that for a principal ideal in $O_K$ we have $(\alpha)=(\varepsilon^k \alpha)$ where $\varepsilon$ is the fundamental unit

Prove that the preimage of a prime ideal is also prime.

A finite dimensional algebra over a field has only finitely many prime ideals and all of them are maximal [duplicate]

Why do we study prime ideals?

Does the polynomial belong to the ideal

Unique factorization domain and principal ideals

Methods to check if an ideal of a polynomial ring is prime or at least radical

Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma

Cardinality of quotient ring $\mathbb{Z_6}[X]/(2X+4)$

Existence of minimal prime ideal contained in given prime ideal and containing a given subset

Ideal contained in a finite union of prime ideals

Number of elements in the ring $\mathbb Z [i]/\langle 2+2i\rangle$

Ideal of the twisted cubic

How does a Class group measure the failure of Unique factorization?

Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$

A maximal ideal is always a prime ideal?

Show that a radical ideal has no embedded prime ideals. [closed]

New posts in ideals

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

Can the square of a proper ideal be equal to the ideal?

If an ideal contains the multiplicative identity, then it is the whole ring

Show that for a principal ideal in $O_K$ we have $(\alpha)=(\varepsilon^k \alpha)$ where $\varepsilon$ is the fundamental unit

Prove that the preimage of a prime ideal is also prime.

A finite dimensional algebra over a field has only finitely many prime ideals and all of them are maximal [duplicate]

Why do we study prime ideals?

Does the polynomial belong to the ideal

Unique factorization domain and principal ideals

Methods to check if an ideal of a polynomial ring is prime or at least radical

Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma

Cardinality of quotient ring $\mathbb{Z_6}[X]/(2X+4)$

Existence of minimal prime ideal contained in given prime ideal and containing a given subset

Ideal contained in a finite union of prime ideals

Number of elements in the ring $\mathbb Z [i]/\langle 2+2i\rangle$

Ideal of the twisted cubic

How does a Class group measure the failure of Unique factorization?

Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$

A maximal ideal is always a prime ideal?

Show that a radical ideal has no embedded prime ideals. [closed]