Talk:Universal algebra
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| Mathematics grading: | Start Class | Mid Importance | Field: Algebra | ||
| Needs information on applications, major theorems; plus further information on homomorphism and more examples Tompw 15:11, 5 October 2006 (UTC) | |||||
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Universal algebra is a former good article candidate. There are suggestions below for which areas need improvement to satisfy the good article criteria. Once the objections are addressed, the article can be renominated as a good article. If you disagree with the objections, you can seek a review.
Date of review: No date specified. Please edit template call function as follows: {{FailedGA|insert date in any format here}} |
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[edit] Details
Currently, the entry I've created for Yde Venema is likely to be deleted on the grounds that it's an insignificant biographical entries. Thoughts?
jtvisona 03:13, 7 Aug 2003 (UTC)
Yes, a thought! Who is "Yde Venema" and what makes him or her worth quoting? This quotation, if kept, does not belong in the rather nice introduction. Zaslav 18:37, 25 June 2006 (UTC)
[edit] Range and organization of subject
It seems to me that this article deals with algebras in the sense of universal algebras (algebraic structures) rather than universal algebra as a branch of mathematics. I think that the current content should be merged with the content of the article algebraic structure. The article about the branch of mathematics should not define and describe algebraic structures but present the history of the branch and its important results, and its title perhaps should be "Theory of universal algebras" to avoid confusion. Andres 08:33, 12 Apr 2004 (UTC)
Disagree. History can be added to the page, but the suggested merge isn't an improvement, in my opinion.
Charles Matthews 11:25, 12 Apr 2004 (UTC)
- Let me explain this again. There are different concepts, such as group and group theory or topological space and topology. Analogously, universal algebra aka algebra aka algebraic structure is different concept from universal algebra as a branch of mathematics, and therefore I think they deserve different articles. Currently, in the present article most talk is about universal algebras. I think this part of the article should be merged with the content of the article Algebraic structure. True, there still is a Bourbakian concept of algebraic structure, but nothing effectively is said about it in that article. There is a terminological mess in this field but I think the first step could be such a reorganization of material, the second step would be finding the adequate titles. Then a formal definition of a (universal) algebra could be given involving signatures. And further, more information about the topic could be given. But I would not go for it before the organization of material is clear. Please explain why you think this wouldn't be an improvement. Andres 14:31, 12 Apr 2004 (UTC)
I do know the distinction you are making. But if 'universal algebra' is a little ambiguous, we should still discuss this all on one page. The situation is similar with tensor algebra. This can mean two things. In the end the page might need to be split up; but there is no hurry about that.
Charles Matthews 15:51, 12 Apr 2004 (UTC)
This article is too brief to indicate the breadth of the results of universal algebra Yes it is... but that is no excuse not to add more to indicate this breadth - Wikipedia is not a paper encyclopedia. Tompw 00:03, 23 December 2005 (UTC)
I removed the section on modules, containing only a confusing link to a redirected page. Spakoj 09:49, 12 January 2006 (UTC)
[edit] Article removed from Wikipedia:Good articles
This article was formerly listed as a good article, but was removed from the listing because the article lists none of its references or sources --Allen3 talk 20:36, 18 February 2006 (UTC)
I failed the current GA nomination because the intoduction needs to be fleshed out, the connections to other mathmatical topics expanded, the history of the concept mentioned, and more sources cited. Ideally the explanations and examples could also be made more clear for the non-specialist, but that is very difficult in these specialized topics. Eluchil404 01:06, 26 April 2006 (UTC)
[edit] "not allowed"
Please do not claim that the definition of a universal algebra only allows universally quantified equations. This is simply not true.
- A universal algebra is a set equipped with operations. These operations may or may not satisfy certain "laws" (universally quantified equations), and they also may or may not satisfy certain other properties.
- It is true that in the field of Universal Algebra (I write it with capital letters to distinguish it from the objects, the universal algebras), varieties play an important role, and that varieties are classes of algebras defined by universally quantified equations.
- It is also true that in universal algebra it is often more convenient to define groups as structures with signature (2,1,0) rather than as structures of type (2) (group multiplication), because that makes them into a variety.
- But mathematicians working in the field of Universal Algebra are also interested in many classes of universal algebras that are not (and in fact cannot be) defined by equations. Off the top of my head: fields; complete lattices; atomic or atomless Boolean algebras; locally finite structures; subdirectly irreducible elements of your favorite variety; etc.
Aleph4 19:24, 25 June 2006 (UTC)
