Newbetuts

Show that the set generated by $A$ is $\{r_1a_1+r_2a_1+ \dots +r_ka_k \mid k \in \Bbb N, r_i \in R, a_i \in A, i \le k\}.$

If $I \subseteq \sqrt{J}$, then there is an $n \in \mathbb{N}$ such that $I^n \subseteq J$

Quotient of free module

Extension of intersection of ideals

For a ring R, and ideals $A$, $B$, then $AB=A \cap B$ if $A + B = R$

fields are characterized by the property of having exactly 2 ideals [duplicate]

When an Intersection of Prime Ideals is a Prime Ideal

Failure of existence of GCD

Inverse image of prime ideal in noncommutative ring

Proving $\pi$ is irreducible/prime in $R.$

Prove that ring contains infinitely many minimal prime ideals

Ideal of $\mathbb{C}[x,y]$ not generated by two elements

Prove the increasing union of ideals is an ideal

What is the significance of the quotient $m/m^2$?

$k[x,y]/(xy-1)$ isomorphic to $k[x,\frac{1}{x}]$ [duplicate]

For every prime ideal $p$ the local ring $R_p$ has no nilpotent elements, then $R$ has no nilpotent elements

What is the quotient $\mathbb Z[\sqrt{3}]/(1+2\sqrt{3})$?

New posts in ideals

Can a local ring have more than one prime ideal?

$Rad(I)$ is an ideal of $R$

Quotient Ring with kernel?

Show that the set generated by $A$ is $\{r_1a_1+r_2a_1+ \dots +r_ka_k \mid k \in \Bbb N, r_i \in R, a_i \in A, i \le k\}.$

If $I \subseteq \sqrt{J}$, then there is an $n \in \mathbb{N}$ such that $I^n \subseteq J$

Quotient of free module

Extension of intersection of ideals

For a ring R, and ideals $A$, $B$, then $AB=A \cap B$ if $A + B = R$

fields are characterized by the property of having exactly 2 ideals [duplicate]

When an Intersection of Prime Ideals is a Prime Ideal

Failure of existence of GCD

Inverse image of prime ideal in noncommutative ring

Proving $\pi$ is irreducible/prime in $R.$

Prove that ring contains infinitely many minimal prime ideals

Ideal of $\mathbb{C}[x,y]$ not generated by two elements

Prove the increasing union of ideals is an ideal

What is the significance of the quotient $m/m^2$?

$k[x,y]/(xy-1)$ isomorphic to $k[x,\frac{1}{x}]$ [duplicate]

For every prime ideal $p$ the local ring $R_p$ has no nilpotent elements, then $R$ has no nilpotent elements

What is the quotient $\mathbb Z[\sqrt{3}]/(1+2\sqrt{3})$?