Talk:Principal ideal domain

ZFC-centrism[edit]

It might be worth mentioning that the claim that every PID is a UFD is not generally true in ZF. There's actually a proof that ZF is consistent with the existence of a PID which is not UFD in Hodges' "Model theory". — Preceding unsigned comment added by 79.183.131.103 (talk) 10:35, 17 December 2013 (UTC)[reply]

rating update[edit]

How about updating the rating of this article? This is no stub. I would say, it is B. What do you think? Spaetzle (talk) 13:59, 16 February 2012 (UTC)[reply]

Proof for example[edit]

A proof of the example given of a PID that is not an ED would be nice. —Preceding unsigned comment added by Ecorcoran (talk • contribs) 1 December 2004

I'm sure it's given in Wilson, J. C. "A Principal Ring that is Not a Euclidean Ring." Math. Mag. 34-38, 1973... 129.97.45.36 09:42, 14 December 2006 (UTC)[reply]

Structure theorem[edit]

might be nice to mention the structure theorem for PID's too. —Preceding unsigned comment added by 171.66.56.36 (talk • contribs) 23 March 2007

Which structure theorem? --345Kai (talk) 00:01, 25 March 2009 (UTC)[reply]

Definition set off[edit]

A defintion of a PID that is set off from the rest of the paragraph would be nice also. —Preceding unsigned comment added by 209.43.8.56 (talk) 15:24, 3 September 2007 (UTC)[reply]

leader[edit]

I rewrote the leading paragraphs: they contained a lot of stuff about rings and ideals in general: this is not the place for that. I put stuff more pertinent to PIDs, instead.--345Kai 04:43, 19 October 2007 (UTC)[reply]

String of class inclusions is Dedekindist[edit]

I really don't like the following. It singles out the UFD property of PID as opposed to other properties, like one-dimensionality (Dedekind). --345Kai (talk) 23:54, 24 March 2009 (UTC)[reply]

Principal ideal domains fit into the following (not necessarily exhaustive) chain of class inclusions:

Commutative rings ⊃ integral domains ⊃ integrally closed domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields

OK, so I got rid of the string of class inclusions, and replaced it with prose which is less partial.--345Kai (talk) 00:10, 25 March 2009 (UTC)[reply]

Is $\mathbb {Z} _{2}^{\infty }$ a Principal ideal domain?[edit]

Moved from Wikipedia:Reference desk

– Hkhk59333 (talk ) 08:51, 20 May 2010 (UTC)[reply]

Is $\mathbb {Z} _{2}^{\infty }$ a Principal ideal domain? Hkhk59333 (talk ) 08:51, 20 May 2010 (UTC)[reply]

This is a question for WP:RD/Math, not here. When you ask it there, make sure you explain what

\mathbb {Z} _{2}^{\infty }

is supposed to mean. Algebraist 09:07, 20 May 2010 (UTC)[reply]