Talk:Semiring

message: 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)

message: 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)
thread_title:  Merge with [[Rig (algebra)]] 

message: 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)
thread_title:  Problem with skew lattice example 

message: 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)
replies: text: Not quite. The additive identity law says that x plus zero is x for all x, but you've got b plus zero being equal to zero (it should be equal to b). Hdgarrood (talk) 16:44, 3 February 2019 (UTC)
replies: text: Actually, I think b +0=0 is just a typo; correcting it to b+0=b still leads to the conclusion ab = ab + a0. The real problem is that we cannot conclude from this that a0 = 0 holds: for that we would need that \forall x,y: x+y=x \implies y=0, i.e., a form of cancellation property. Proving that normally is done by subtracting x from both sides, which we can't do here. Indeed, I believe a counterexample can be obtained by modifying the extended natural numbers slightly: change the rule 0\cdot \infty=0 to  0\cdot \infty=\infty. The result seems to satisfy all axioms of a semiring as given here, except for the final one (0 does not annihilate the whole ring)  BlackFingolfin (talk) 09:42, 20 May 2021 (UTC)
thread_title:  Problem with semiring definition 

message: 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)
replies: text: 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)
thread_title:  Should bibliography be changed to references? 

message: 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 is a quote from Proofwiki.org's definition of  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)
replies: text: 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)
thread_title:  General Question on Math Standarization 

message: 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: ! JMP EAX (talk) 07:32, 18 August 2014 (UTC)
replies: text: 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)
thread_title:  Tropical semiring 

message: The usual definition of dioid is an idempotent semiring: that is, a+a=a.  However, Gondran and Minoux (2008) p.28 define them in such a way that N,+,× is a dioid.  Is there a usefdul terminolgy current for the two defnitions?  Deltahedron (talk) 15:55, 19 August 2014 (UTC)
thread_title:  Dioid 

message: I'm pretty sure that Endo isn't a full semiring, as composition doesn't distribute left over point wise addition:
f _ = 1
g _ = 1
h _ = 0
f . (g + h) = (f . g) + (f . h)
1 = 1 + 1
It's a near-semiring, I think. 
Doisin (talk) 16:39, 3 November 2016 (UTC)
replies: text: Endomorphisms of a commutative monoid do form a semiring.  Your f is not an endomorphism. 67.86.129.121 (talk) 02:01, 3 October 2022 (UTC)
thread_title:  Is Endo a semiring? 

message: Rings without additive inverses or multiplicative identities. Alfa-ketosav (talk) 13:50, 26 April 2019 (UTC)
thread_title:  Rgs 

message: Hi, is there such a thing as a near-miss of a ring that is not necessarily a ring because it doesn't necessarily have additive invertibility, but it does have additive cancellation? In other words, a + c = b + c implies a = b, even though c need not have an inverse. Then the multiplicative annihilator property could still be proven instead of assumed. OneWeirdDude (talk) 18:35, 28 June 2020 (UTC)
thread_title:  Alternative definition? 

message: What's this definition doing in this article? If there's any relationship between the set-theoretic structure and the algebraic structure it should be clarified, otherwise this should be moved elsewhere. viiii (talk) 04:53, 20 March 2024 (UTC)
replies: text: Indeed.—Emil J. 10:13, 20 March 2024 (UTC)
thread_title:  Semiring of sets