User talk:Barto

Splitting Theorem and Definition
Thanks for your work on Definition:Z-Module Associated with Abelian Group, it was long overdue.

In the future, please take care to duplicate any sources listed on the original integrated page on both resultants, and flag them with Template:SourceReview. This way, we can ensure to continue representing the content of said sources as faithfully as possible.

If applicable, please also attend to any links to the page via "Tools -> What links here" in the sidebar menu. They might have to be updated to the new definition. &mdash; Lord_Farin (talk) 16:46, 5 December 2016 (EST)


 * I'll keep it in mind.--barto (talk) 03:24, 6 December 2016 (EST)


 * Also please note the wording of the SourceReview template, with particular reference to the word "following". It is how we distinguish between sources which have been reviewed and those we have not. --prime mover (talk) 06:56, 6 December 2016 (EST)

Consistent naming
Thank you for taking the time and effort to improve the structure of this area -- it is long overdue.

The reason for inconsistent naming between e.g. direct product of groups and direct sum of rings is purely as a result of the source works that the material came from.

The definition namespace of was conceived more or less as a dictionary of existing usage, and as such we make the effort to stick to what is found in the source works which are plundered to provide material. If it just so happens that the source work used uses "sum", then that, by default, is what was taken.

So I don't think there are problems with renaming Ring Direct Sum to Ring Direct Product, and I don't think there are many pages that would need to be changed to accommodate it. As is our usual technique, we can of course use "Also known as" to explain the differences in terminology.

As for removing "external" from all "external direct product" pages -- again, I think that should be okay. I was specifically using "external" as opposed to "internal" as I had trouble with this when first studying group theory and I needed to make sure I was very sure what was being discussed -- particularly when I was battling with the Internal Direct Product Theorem -- but now I look back on it, I think we would be okay to just use "Direct Product" for what is now "External Direct Product", using an "also known as" section to explain the alternative terms. --prime mover (talk) 06:53, 17 December 2016 (EST)


 * Thank you for your assistance! Indeed, because for finite families they coincide, different authors may (rightfully!) use different names if they do not consider the infinite case. As for External: While I do prefer "Direct Product" over "External Direct Product"; I would not mind if page names include "External" as long as there are appropriate redirects to them. As for Internal Sum vs. Internal Product: Both are used and mean the same (at least for groups, rings, modules). Naturally, sum is reserved for the commutative case; that is, for modules (and vector spaces), while product is used in the non-commutative case (so more fitting for groups and rings). The reason we do not make a distinction between internal direct sum and internal direct product is that within a structure, we cannot take infinite sums/products --barto (talk) 07:07, 17 December 2016 (EST)


 * You seem to have a far better handle on this than me, who, since my MMath, my entire knowledge is self-learned and haphazard. Feel free to go ahead, as you know where the devils are in the details. --prime mover (talk) 07:10, 17 December 2016 (EST)


 * Before we start renaming pages: do we go for X Direct Product (as in Definition:Module Direct Product and many others) or Direct Product of X'es (as in Definition:External Direct Sum of Rings and Product of Vector Spaces )? Are there cons of Direct Product of X'es besides alphabetic ordering? --barto (talk) 08:12, 17 December 2016 (EST)


 * I believe that "Group Direct Product" is a standard term used commonly in AbAlg and Group Theory as I have seen it a few times in source works. I don't know about modules. My gut tells me to go with whatever is most "standard" and if that means naming is inconsistent, then that is of less importance than intellectual accessibility, but it is not a point I feel strongly about. If you feel it would be an improvement to be consistent, then DP of Xs works better for me as a general standard than XDP. Others may differ, but it is up to them to express an opinion, and if they don't it is assumed they may not be strongly concerned either way. --prime mover (talk) 08:23, 17 December 2016 (EST)

I vote DP of Xs. Looking at your ambitious plans, one point of attention is the approach of universal properties. Because there is always the open point of integrating all this with the category-theoretic perspective one day, where of course the universal property is the defining concept, and the abstract-algebraic definition is a means of fulfilling this definition.

But maybe it's not a thing that realistically can be incorporated at this point. Feel free to proceed even if you're not able to come up with a universal approach (heh ;)). &mdash; Lord_Farin (talk) 15:53, 18 December 2016 (EST)

Making the definitions more complicated
We have a specific policy on to put only definitions in a definition page, and not clutter it up with justifications for the validity of the definition. If there is a genuine need to justify the existence of an object because it is non-intuitive, then we add it as a separate proof page.

Hence I reversed out your additions to Ceiling and Floor definitions. --prime mover (talk) 01:11, 29 January 2017 (EST)


 * Okay. What about adding just one sentence to the definition, just to link to a page where it is shown that the definition is valid? --barto (talk) 03:38, 29 January 2017 (EST)


 * See the "Also see" section. --prime mover (talk) 04:31, 29 January 2017 (EST)

Continued good work
I appreciate the way you've got the general "feel" of and you're generating some seriously worthwhile content.

Please do not feel offended if I (or others) spontaneously amend (or even reverse out) some of your changes, or change the notation, presentational style and even source code style in ways which may look arbitrary. It's all working towards completely consistency of content and structure. --prime mover (talk) 16:23, 23 April 2017 (EDT)


 * No problem. I'm happy to contribute, especially if it's things you most likely won't find anywhere else (because nobody has made the effort to write out a proof). Of all the small amendments I can think of only one I dislike, which is the use of  for every pair of brackets. It creates additional spacing before the brackets, which I don't find aesthetic: $f\left(x\right)$ vs. $f(x)$, or worse: $\gcd\left(a,b\right)$ vs $\gcd(a,b)$. It's as if the $\gcd$ has nothing to do with $(a,b)$.  --barto (talk) 16:31, 23 April 2017 (EDT)


 * You're not alone, nobody likes the \left...\right. :-) OTOH I personally do prefer the extra gap before the brackets. This is one area where not everybody is going to be happy.


 * Oh yeah -- I was actually taught $\gcd \left\{ {a, b}\right\}$ because "it doesn't matter what order the operands go in". There are (generally unresolved) debates about the general wisdom of using set notation for such argument lists throughout the talk pages of . --prime mover (talk) 16:38, 23 April 2017 (EDT)


 * I imagine. What was the motivation to begin to use set notation, except the fact that we can? Does a certain author use this? I don't like it neither, because it hides things like $\gcd(a,b,b,a,b)=\gcd(a,b)$ (and not only $\gcd(a,b)=\gcd(b,a)$). Also, in general rings (that are not $\Z$ or polynomial rings over fields), $\gcd(a,b)$ becomes the ideal $(a,b)$, and then we use round brackets and not set notation for obvious reasons. --barto (talk) 16:50, 23 April 2017 (EDT)


 * I think it came from my M203 course in my MMath (OTOH might have been the Number Theory module). Didn't much like it, but thought that was the way it should be done. That was the same course that liked $]a, b[$ for an open interval, which I really didn't like.


 * In general we are trying to use the most up-to-date notation we can find which is not too specialised, trying at the same time to pick notation which is as unambiguous as possible, even if this means not using the most conventional notation. Hence the need to define the notation when it is being used: "where $a \mathrel \backslash b$ denotes that $a$ is a divisor of $b$" and so on. --prime mover (talk) 16:58, 23 April 2017 (EDT)