Newbetuts

If the localization of a ring $R$ at every prime ideal is an integral domain, must $R$ be an integral domain?

Intersection of finitely generated ideals

In a finite ring extension there are only finitely many prime ideals lying over a given prime ideal [duplicate]

Ring of formal power series over a field is a principal ideal domain

One-to-one correspondence of ideals in the quotient also extends to prime ideals?

Ideals in direct product of rings [duplicate]

Show $\mathbb Z[x]/(x^2-cx) \ncong \mathbb Z \times \mathbb Z$.

An ideal whose radical is maximal is primary

Construct ideals in $\mathbb Z[x]$ with a given least number of generators

Why is $(2, 1+\sqrt{-5})$ not principal?

In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?

The set of all nilpotent elements is an ideal

Let $R$ be a commutative Noetherian ring (with unity), and let $I$ be an ideal of $R$ such that $R/I \cong R$. Then is $I=(0)$?

Primary decomposition of a monomial ideal

if R is a commutative ring in which all the prime ideals are finitely generated then R is Noetherian [duplicate]

What's the motivation of the definition of primary ideals?

New posts in ideals

Primary ideals in Noetherian rings

Simple example of non-arithmetic ring (non-distributive ideal lattice)

Converse to Chinese Remainder Theorem

$\mathbb Z\times\mathbb Z$ is principal but is not a PID

If the localization of a ring $R$ at every prime ideal is an integral domain, must $R$ be an integral domain?

Intersection of finitely generated ideals

In a finite ring extension there are only finitely many prime ideals lying over a given prime ideal [duplicate]

Ring of formal power series over a field is a principal ideal domain

One-to-one correspondence of ideals in the quotient also extends to prime ideals?

Ideals in direct product of rings [duplicate]

Show $\mathbb Z[x]/(x^2-cx) \ncong \mathbb Z \times \mathbb Z$.

An ideal whose radical is maximal is primary

Construct ideals in $\mathbb Z[x]$ with a given least number of generators

Why is $(2, 1+\sqrt{-5})$ not principal?

In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?

The set of all nilpotent elements is an ideal

Let $R$ be a commutative Noetherian ring (with unity), and let $I$ be an ideal of $R$ such that $R/I \cong R$. Then is $I=(0)$?

Primary decomposition of a monomial ideal

if R is a commutative ring in which all the prime ideals are finitely generated then R is Noetherian [duplicate]

What's the motivation of the definition of primary ideals?