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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)
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)
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)
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)
—
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 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)
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." [1] 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)
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)
"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)
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)
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)
I think possibly there is some textbook somewhere that lists Endo as a semiring, possibly because they don't include left distribution as a semiring law. (And that's why the correction keeps getting removed). It might be useful to include the short example above to demonstrate that Endo isn't a semiring according to this article's definition of semirings.
Doisin ( talk) 12:07, 19 February 2022 (UTC)
I've noticed that most articles on algebraic structures have a section called properties, where commonly useful consequences of the structure's axioms are listed. Maybe someone familiar with semi-ring theory could add such a section?
Rings without additive inverses or multiplicative identities. Alfa-ketosav ( talk) 13:50, 26 April 2019 (UTC)
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)
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)
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
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)
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)
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)
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)
—
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 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)
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." [1] 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)
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)
"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)
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)
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)
I think possibly there is some textbook somewhere that lists Endo as a semiring, possibly because they don't include left distribution as a semiring law. (And that's why the correction keeps getting removed). It might be useful to include the short example above to demonstrate that Endo isn't a semiring according to this article's definition of semirings.
Doisin ( talk) 12:07, 19 February 2022 (UTC)
I've noticed that most articles on algebraic structures have a section called properties, where commonly useful consequences of the structure's axioms are listed. Maybe someone familiar with semi-ring theory could add such a section?
Rings without additive inverses or multiplicative identities. Alfa-ketosav ( talk) 13:50, 26 April 2019 (UTC)
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)
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)