From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2260 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: equivalent varieties Date: Mon, 28 Apr 2003 11:50:59 +0100 (BST) Message-ID: References: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018532 3294 80.91.229.2 (29 Apr 2009 15:22:12 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:22:12 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Apr 28 09:06:53 2003 -0300 X-Keywords: Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 28 Apr 2003 09:06:53 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19A7Ov-0006vs-00 for categories-list@mta.ca; Mon, 28 Apr 2003 09:06:29 -0300 In-Reply-To: X-Scanner: exiscan for exim4 (http://duncanthrax.net/exiscan/) *19A6Ds-0000od-DP*O/rXfW8/Lfk* Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 21 Xref: news.gmane.org gmane.science.mathematics.categories:2260 Archived-At: On Sat, 26 Apr 2003, Prof. Peter Johnstone wrote: > The equivalence of these varieties for all p is well known. It's best > understood by seeing that they are all dual to the category of Stone > spaces: given a Stone space, the ring of continuous Z_p-valued functions > on it (where Z_p is given the discrete topology) is a ring satisfying > p1=0 and x^p=x; conversely, given such a ring, its prime (=maximal) > ideal spectrum is a Stone space. > > Not having my copy of "Stone Spaces" to hand as I write this, I can't > remember whether this fact was in the book. But it certainly should have > been. > Yes, it is there -- Exercise V 2.6, page 186. Peter Johnstone