User talk:Barto

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Cheers! prime mover (talk) 13:43, 3 December 2016 (EST)

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)