Talk:Medial magma

July 2006
I just finished a major edit of this page. I reintroduced the magma terminology (because "medial algebra" isn't used in practice), added examples, and made various other improvements. An earlier discussion about the cartesian square of the operation was confusing, because that is not an endomorphism, it's a homomorphism. I hope the present discussion is clearer.

What I'd still like to add is a section describing the Toyoda-Bruck theorem (it characterizes medial quasigroups in terms of abelian groups) and some remarks about the mode/modal terminology of Romanowska and Smith. I'm not sure when I'll have time to do this, though. --Michael Kinyon 00:33, 31 July 2006 (UTC)

Requested move

 * The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section. 

The result of the move request was: move to Medial magma. It's not at all clear which between "medial magma" or "medial algebra" should be the name of the article (as I am nothing remotely close to an expert on this topic), but I'm going to go with the original proposed title over the latter given "medial algebra" doesn't currently appear in the article. If the article can be expanded to the scope that makes "medial algebra" a more appropriate title, I have no objection to it being moved accordingly. --  tariq abjotu  05:26, 12 August 2013 (UTC)

Medial → Medial magma – The concept discussed here does not appear to be the main use of medial on Wikipedia, as can be seen by Special:WhatLinksHere/Medial. Most people linking to this page appear to intend various anatomy terms, with a few intending the mathematics concept described here, as well as some other "middle" things. I hope mathematicians can decide whether Medial magma, Medial identity, or some other name is most appropriate. Cnilep (talk) 02:11, 30 July 2013 (UTC)
 * Support some rename. Replace with disambiguation page -- 76.65.128.222 (talk) 04:35, 30 July 2013 (UTC)
 * Support medial magma algebra and change medial to be a disambig page. Dicklyon (talk) 05:46, 30 July 2013 (UTC)
 * Support. Move media to medial magma.  A disambiguation is not necessary if the only other target is Anatomical terms of location (to which lateral and medial redirects).  For that a disambiguating hatnote at the top of the section should suffice.   Sławomir Biały  (talk) 11:50, 30 July 2013 (UTC)
 * A dab page already exists. Make it the primary target; Sławomir’s proposal (a dab hatnote somewhere deep in an article) would complicate navigation. Incnis Mrsi (talk) 12:02, 30 July 2013 (UTC)
 * Yes, that's better. Sławomir Biały  (talk) 12:30, 30 July 2013 (UTC)


 * Support. In general, article names should be nouns (perhaps with adjectives attached) rather than adjectives. RDBury (talk) 19:42, 30 July 2013 (UTC)
 * Comment: the term medial algebra is used, contrary to the July 2006 comment above, and denotes a generalisation of this concept  Perhaps a move to an article Medial algebra expounding the theorem that any medial algebra in varieties in which every algebra has a modular lattice of congruences) can be represented as a module over a commutative ring?  Spectral sequence (talk) 20:10, 30 July 2013 (UTC)
 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Bruck
Honestly I'm miffed why a number of papers attribute the result to Bruck (as well) because Bruck's paper says "First it is shown that every abelian quasigroup is isotopic to an abelian group, unique in the sense of isomorphism (Theorem 11). This result is essentially Murdoch's." 86.127.138.234 (talk) 11:41, 23 February 2015 (UTC)

On the other hand, at start of section 10, Bruck says "With the exception of the last theorem of the section, the results are essentially due to Murdoch", and unless I am mistaken, the last theorem is indeed the Toyoda theorem (Theorem 11). After browsing a few seconds through Murdoch's paper, I cannot see where Murdoch clearly wrote the equivalent of Theorem 11 2A01:E35:8ABC:B3D0:B0C5:F9A7:5F0D:1690 (talk) 01:44, 12 August 2015 (UTC)

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Merger proposal
I propose merging Category of medial magmas into Medial magma. This is in line with the example given by Group (mathematics). While there is also Group theory for a more advanced treatment, category-theoretic topics like homomorphisms and products are discussed on the elementary group theory page and there is no article on the category/variety of groups itself. On the other hand, both Ring (mathematics) and Category of rings exist. The latter article is a list of unsourced properties with little exposition, however, which leans in favor of merging/eliminating these "category of blahs" articles unless they can be better justified separately from "blahs" themselves.caterpillar_tree (talk) 02:42, 16 January 2022 (UTC)