Talk:Semiring

The Mathworld URL doesn't work for me (right now).

Is importing this from Mathworld (a) OK and (b) worth it?

Charles Matthews 09:20, 20 Nov 2003 (UTC)

Merge with Rig (algebra)

Every reference on semirings that I can find (besides the always dubious MathWorld) defines them to include 0 and 1. Which means this is the same concept as that defined at rig (algebra). Moreover, I can find numerous references on semirings but almost none on rigs. Is this a term that is really used? In any case it seems that "semiring" is more common and "rig" should be redirected here and not the other way around. Comments, objections? -- Fropuff 23:54, 2004 Jul 23 (UTC)

Isn't rig used by John Baez? And isn't that the only obvious reason it made it into WP?

Charles Matthews 02:43, 24 Jul 2004 (UTC)

Ahh... there's a theory. I think you may be right. Baez appears to use rig frequently. See "This Week's Finds in Mathematical Physics" 121, 185, 191. His own comment on the matter: [1]. In any case I think I will merge the articles. -- Fropuff 03:47, 2004 Jul 24 (UTC)

Problem with skew lattice example

As an example of a semiring, a skew lattice on a ring is stated. But the operation a+b+ba-aba-bab is not associative in general, thus a skew lattice may not be a semiring. I am not an expert so I did not delete this - if you are an expert and agree, please delete it. --90.180.188.114 (talk) 05:44, 4 May 2012 (UTC)

Problem with semiring definition

This property appears in the semiring definition:

 4. Multiplication by 0 annihilates R: 0·a = a·0 = 0

But according to the ring definition http://en.wikipedia.org/wiki/Ring_(mathematics) that property is not required. And the only difference between a ring and a semiring is the lack of inverse. This property does not appear in Mathworld: http://mathworld.wolfram.com/Semiring.html — Preceding unsigned comment added by Melopsitaco (talk • contribs) 00:19, 1 November 2012‎ (UTC)

Rings satisfy this property automatically, it follows from distributivity and the existence of additive inverses, so that’s why it is not stated there explicitly. Mathworld is well known for numerous errors, and the definition we have is properly sourced.—Emil J. 13:42, 1 November 2012 (UTC)

—

But doesn't this annihilation axiom 4 also follow here, for semirings, from distributivity and additive identity?:

distributivity:
   a(b+c) = ab + ac
assume c=0:
=> a(b+0) = ab + a0
additive identity:
    (b+0) = 0
=> a(b)   = ab + a0

If a0 != 0 (axiom 4), distributivity is unsatisfied.

NB: I'm really asking. I'm not an expert -- 20:32, 17 November 2013 (UTC)

Should bibliography be changed to references?

Should bibliography section be changed to a reference section? Or should the footnotes be made into the reference section while the general sources be left as bibliography?

In general, of the pages I have seen on wikipedia, there does not seem to be any standard way to categorize references. I've seen "footnotes", "references", "bibliography", "notes", etc. as headers and with different content under them. Pages also have different combinations of there headers; some having "notes" and "references" with "notes" being references that are footnotes, some use "notes" for non-reference notes only, etc.

Is there some standard way of doing this that is documented? Shouldn't there be?

This is my first post in any talk section coming after my first edit of an article (this one) so I apologize for my ignorance. I added the only non-reference footnote to this page and that is what sparked this question. For now I will add a "notes" section just so there isn't a random non-bibliographic note in the "bibliography" section... Dosithee (talk) 19:46, 1 January 2013 (UTC)

This is covered by the Wikipedia:Manual of Style, especially at Wikipedia:Manual_of_Style/Layout#Notes_and_References. "Bibliography" is an alternative for "References". Deltahedron (talk) 20:05, 1 January 2013 (UTC)

General Question on Math Standarization

Are there really no standard definitions of mathematical terms? Everything from the definition of range to semiring seems to have different definitions depending on the source. And there is also the issue of multiple names for the same thing like "one-one (or 1-1) or one-to-one for injective, and one-one mapping or one-to-one mapping for injection." This seems like a large issue in terms of its effects on clarity and thus learning and expresion. It seems there must have been some conference or something on this at some point but I cant find any.

Dosithee (talk) 20:07, 1 January 2013 (UTC)

Do you mean standard in the world at large, or on Wikpedia? In either case the answer is no, but a general question like this would be better addressed at Wikipedia talk:WikiProject Mathematics. Deltahedron (talk) 20:10, 1 January 2013 (UTC)

Tropical semiring

There are several defs of that in various sources but the source cited [only] gives a 3rd one [not given in this wiki article], with the whole extended real line: [2]! JMP EAX (talk) 07:32, 18 August 2014 (UTC)

The text and the table on that page are incconsistent: the definition in the article is that of the text. It would be good to find a reliable source that sorted out the various definitions that exist in the literature. Deltahedron (talk) 08:16, 18 August 2014 (UTC) Meanwhile, I have expanded the text with reference for the other definition. Deltahedron (talk) 09:26, 18 August 2014 (UTC)

Star semiring

"To make * actually act like the usual Kleene star, a more elaborate notion of complete star semiring is needed." is a little clumsy, as it implies the object is to make the asterate as close as possible to the Kleene star. Deltahedron (talk) 09:28, 18 August 2014 (UTC)

I have reordered the material to present the more complicated algebraic structure towards the end, and moved some text to Monoid#Complete monoids which seems a more natural target for the redirect Complete monoid which was otherwise circular. Deltahedron (talk) 14:05, 18 August 2014 (UTC)

Maybe you should have considered that the "more complicated" isn't really so. There's a reason these notions are introduced in a certain order in WP:RS. I have reverted your "improvement" as it completely messed up the logic of the presentation, giving overpowered examples for trivial notions like for simply adding a unary operation. JMP EAX (talk) 23:51, 18 August 2014 (UTC)

An algebraic structure with additonal operations may reasonably be considered "more complicated". Please explain the reason for the order of the presentation in the source as you see it, and what the logic of the presentation is that you feel has been messed up. Deltahedron (talk) 06:21, 19 August 2014 (UTC)