Talk:Outline of algebraic structures

message: I have had nothing to do with the content of "Allowing additional structure"; that's 100% legacy.
:Heh, I'm afraid that rather inelegant legacy is partially mine; I created the section to deal with sets with structure other than operations that had been included by a still earlier editor. Such is the evolution of an article... Probably it should be recombined with "Structures that are not varieties", which already deals with such non-operations as norms, inner products, and gradings. Melchoir 03:55, 19 July 2006 (UTC)
replies: text: I would be fine with combining them, as long as there remains a clear visual distinction between the two: perhaps colored flags for the entries? Melchoir 07:13, 18 July 2006 (UTC)
replies: text: I would prefer a richer categorization suggested by Jipsen's webpage: varieties, quasivarieties, first order, etc.132.181.160.42 03:48, 19 July 2006 (UTC)
replies: text: I haven't seen it. Got a link? Melchoir 03:56, 19 July 2006 (UTC)
replies: text: It's the sole link at the bottom of the entry! Go ahead and merge in "Allowing additional structure" in any way you see fit.
Let me return to free modules. It is very curious (to me) that modules are varieties but that free modules are not. My orginal description a module mentioned an optional basis. An editor objected that there is no module analog of a vector space basis. A bit of browsing of Birkhoff and MacLane, and I found free modules, which fit the bill. Wikipedia does include an entry named free modules, and my preference is to include in this list every structure described somewhere in Wikipedia. And thus I created a paragraph describing free modules. It is true that there is a free variant of all sorts of algebraic structures, and perhaps this entry should include 1-4 sentences talking about that. Are free algebras properly discussed anywhere in Wiki?
Jipsen mentions structures that I don't quite know how to pigeonhole: hoops come to mind. But all such structures in Jipsen have no Wiki entry to date, so I omit them from this list with a clear conscience!202.36.179.65 11:08, 25 July 2006 (UTC)

text: Let me try to explain what's going on with free algebras. The concept of a free X isn't a "variant" of the concept of an X in the same way a commutative X or an X-with-identity is. Free groups are, for example, comparable to alternating groups. Yes, we can talk about alternating groups in the plural, but the actual definition of an alternating group requires you to pick an n, and once you do so, you're left with a unique object: An. So "alternating group" is just the name of a list of examples. Now, before I go further, just to make sure we're on the same page: would you want to include "Alternating group" in this article? Melchoir 19:38, 25 July 2006 (UTC)
replies: text: Alternating group reveals that it is a type of permutation group of finite order. It is simply a concrete instance of a group and not a distinct algebraic structure. Hence what makes an alternating group distinct from other groups is not its universal algebra structure (the variety group includes alternating groups), but its model theoretic structure. So I see no reason for including it in this list. Good thing, because group theory texts I've been browsing of late reveal a zoo well-stocked with species!202.36.179.65 11:04, 30 July 2006 (UTC)
thread_title:  The fate of "Allowing additional structure" 

message: Would someone well-versed in combinatory logic give my definition of combinatory algebra a close critical reading? The combinatory logic I am to algebraize is, of course, the classic one with S and K primitive. I was inspired to do this by the section "Symbolic Systems" on p. 1172 of Wolfram's A New Kind of Science, but I may be misreading the work of Wolfram and his collaborators.132.181.160.42 01:46, 7 September 2007 (UTC)
thread_title:  Combinatory algebra 

message: Matroids and antimatroids are pretty clearly not varieties. Do they belong here and if so, where? I have put them under lattices that are not varieties, but am very open to moving them elsewhere.132.181.160.42 03:48, 23 October 2007 (UTC)
thread_title:  Matroids, antimatroids: where? 

message: I do not think that this sentence is correct: 
: In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety.
If we accept this definition, the neither the field of rational numbers nor the class of all fields would be an algebraic structure.   
 
I do agree with the terminology in Algebraic structure: 
: An algebraic structure consists of one or more sets, called underlying sets or carriers or sorts, closed under one or more operations, satisfying some axioms.
(Although I do not agree with the emphasis on the axioms.) 
I also do not understand what the editor meant with this sentence: 
: An algebraic structure consists of one or two sets closed under some operations, functions, and relations
# First, it is true that one- and two-sorted structures account for the bulk of algebraic structures that appear in mathematics (e.g. groups are one-sorted, vector spaces two-sorted).  But why not allow more sorts? 
# What is the intended difference between "function" and "relation"? 
# What does it mean to be "closed under a relation"? 
--Aleph4 (talk) 11:06, 24 October 2011 (UTC)
thread_title:  "Is a variety"? 

message: Edit Rejected
Hi! I saw you made an extremely large edit containing some good changes recently. Unfortunately, there were also a lot of questionable changes mixed in. Since the edit was too monolithic to split between the two types, I have reverted it and requested your presence here. It would be nice to carry out the least controversial things first. 
*For sure, I wish the changes to the references could be reproduced. 
*You changed a lot of headers from something like "Two X's and two Y's" to "Two Y'x and two X's". I suppose this is possible, but superficially it seems like a change that doesn't do anything. I could be persuaded, though.
*Massive rewordings of text by a single author are usually viewed with suspicion because they may be heavily influenced by personal views. I don't mean to say you can't write anything like that, but it would be more constructive if we could do a chunk at a time and not every section at once. 
Sorry to slow down your groove... I hope we can reinstate several parts of your edit soon. Rschwieb (talk) 14:18, 12 February 2013 (UTC)
thread_title:  [[User:JP.Martin-Flatin]] 

message: "Outline" is short for "hierarchical outline". There are two types of outlines: sentence outlines (like those you made in school to plan a paper), and topic outlines (like the topical synopses that professors hand out at the beginning of a college course). Outlines on Wikipedia are primarily topic outlines that serve 2 main purposes: they provide taxonomical classification of subjects showing what topics belong to a subject and how they are related to each other (via their placement in the tree structure), and as subject-based tables of contents linked to topics in the encyclopedia. The hierarchy is maintained through the use of heading levels and indented bullets. See Wikipedia:Outlines for a more in-depth explanation.  The Transhumanist 00:02, 9 August 2015 (UTC)
thread_title:  Quick explanation of Wikipedia outlines 

message: Group action is missing from the list.  Since it shares many properties with module-like structures, such as being a set acting in another, such as vector space wich is a field acting in "the vector set" or module wich is a ring acting on "the modules", the group action is a group acting on a set. Now, the set doesn't have to have a operation within. Is that why is not incuded?  — Preceding unsigned comment added by Santropedro (talk • contribs) 18:56, 31 May 2017 (UTC)
thread_title:  "Group action" is missing, it fits well into "module like" structures.