Newbetuts

Looking for a special class of ideals such that If every ascending chain of ideals from this class stabilizes, then $R$ is a Noetherian ring.

Showing that $\lim \sup\limits_{\gamma} \left \|a - a e_{\gamma} \right \| \leq \|a - b\|$ for all $a \in A$ and $b \in J.$

Ideal of ideal needs not to be an ideal

The set of zero divisors is a prime ideal

Showing that $A/J \cong \mathbb C.$

Products of ideals is an ideal and comaximal ideals

Primary decomposition of an ideal (exercise 7.8 in Reid, Undergraduate Commutative Algebra) [duplicate]

In $K[X,Y]$, is the power of any prime also primary?

Checking if $\langle 2 \rangle$ is a maximal ideal in $\mathbb{Z}[i]$

Infinite sum of ideals

prove $(n) \supseteq (m)\iff n\mid m\ $ (contains = divides for principal ideals)

Are $(X+1,X), (X^2+4,5)$ and $(X^2+1,X+2)$ maximal or prime?

If $I$ is a finitely generated ideal of $A[X]$, is $I\cap A$ necessarily finitely generated for a commutative unital ring $A$?

Is there a notation for the set of all ideals of a particular ring?

Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.

If $A/I \cong A/J$ as rings and $I\subseteq J,$ then $I=J.$ [duplicate]

Why is the arbitrary sum, but not the arbitrary intersection, of ideals an ideal?

Showing an ideal is prime in polynomial ring

New posts in ideals

Looking for a special class of ideals such that If every ascending chain of ideals from this class stabilizes, then $R$ is a Noetherian ring.

Prime/maximal ideals of $\mathbb{C}[x, y]$ containing a given ideal

Intuition for ideal quotient / colon ideal?

Showing that $\lim \sup\limits_{\gamma} \left \|a - a e_{\gamma} \right \| \leq \|a - b\|$ for all $a \in A$ and $b \in J.$

Ideal of ideal needs not to be an ideal

The set of zero divisors is a prime ideal

Showing that $A/J \cong \mathbb C.$

Products of ideals is an ideal and comaximal ideals

Primary decomposition of an ideal (exercise 7.8 in Reid, Undergraduate Commutative Algebra) [duplicate]

In $K[X,Y]$, is the power of any prime also primary?

Checking if $\langle 2 \rangle$ is a maximal ideal in $\mathbb{Z}[i]$

Infinite sum of ideals

prove $(n) \supseteq (m)\iff n\mid m\ $ (contains = divides for principal ideals)

Are $(X+1,X), (X^2+4,5)$ and $(X^2+1,X+2)$ maximal or prime?

If $I$ is a finitely generated ideal of $A[X]$, is $I\cap A$ necessarily finitely generated for a commutative unital ring $A$?

Is there a notation for the set of all ideals of a particular ring?

Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.

If $A/I \cong A/J$ as rings and $I\subseteq J,$ then $I=J.$ [duplicate]

Why is the arbitrary sum, but not the arbitrary intersection, of ideals an ideal?

Showing an ideal is prime in polynomial ring