The prufer-domain tag has no wiki summary.

**0**

votes

**1**answer

108 views

### Intersection of powers of prime ideals

Let $R$ be a Noetherian ring. Let $(x)$ be a prime ideal such that $\bigcap_n (x)^n=0$. Then $R$ is a domain.
Is this a known result? I heard its known as the Davis lemma. Can anyone give a ...

**1**

vote

**0**answers

140 views

### On Prüfer domains

Is there any Prüfer domain $R$ that has a prime ideal $P$ that is not finitely generated but $xP$ is subset of a finitely generated ideal $I$,for some $x$ in $R-P$ and $I$⊂$P$?

**4**

votes

**2**answers

218 views

### On Prufer domains

Are there any Prufer domains that have an infinity of prime ideals but only one of those primes is not finitely generated?

**13**

votes

**1**answer

578 views

### Is the ring of all cyclotomic integers a Bezout domain?

My previous question about the theorem (apparently due to Dedekind -- thanks, Arturo Magidin!) that the ring $\overline{\mathbb{Z}}$ of all algebraic integers is a Bezout domain got me thinking about ...