From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3565 Path: news.gmane.org!not-for-mail From: Andrej Bauer Newsgroups: gmane.science.mathematics.categories Subject: Small semirings Date: Wed, 03 Jan 2007 23:09:40 +0100 Message-ID: <8313.01743533022$1241019381@news.gmane.org> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-2; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019380 9278 80.91.229.2 (29 Apr 2009 15:36:20 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:36:20 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Jan 3 18:09:13 2007 -0400 X-Keywords: X-UID: 57 Original-Lines: 30 Xref: news.gmane.org gmane.science.mathematics.categories:3565 Archived-At: Dear categorists, I have no idea where to ask the following algebra question. Hoping that some of you are algebraists, I am asking it here. I am looking for examples of small (finite and with few elements, say up to 8) commutative semirings with unit, by which I mean an algebraic structure which has +, *, 0 and 1, both operations are commutative and * distributes over +. The initial such structure are the natural numbers. Here are the examples I know: 1) Modular arithmetic, i.e., (Z_n, +, *, 0, 1) 2) Distributive lattices with 0 and 1. 3) "Cut-off" semiring, in which we compute like with natural numbers, but if a value exceeds a given constant N, then we cut it off at N. For example, if N = 7 then we would have 3 + 3 = 6, 3 + 6 = 7, 4 * 4 = 7, etc. Do such semirings have a name? There must be a census of small commutative rings, or even semirings. Does anyone know? Andrej