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- --Your friendly ProofWiki WelcomeBot 13:30, 27 December 2012 (UTC)
Your response was helpful. Here is where I found the algebraic structure:
In formal language theory a language is a set of finite sequences called the words of the language.
The head of a language is the set of all prefixes of the words of the language.
I extended this idea with the tail, and centre of a language (defined using suffixes and infixes in the natural way).
Then I treated them as functions and looked at the table of their compositions and came up with the table I posted.
I haven't been able to find where it originally arose but the information you provided was helpful in classifying the aforementioned result for me.
I think it arose from one of my amateur attempts at extending the idea of a field to include 3 operations (back when I knew nothing).
Having said that the paper of Berman and Burris is still out of reach for so until I get the knowledge necessary I am enjoying Jónsdótti and Diego's paper in the mean time.
I've noticed you started to make meaningful contributions to ProofWiki. We are very grateful for the time you have chosen to spare to improve our project. However, it is currently best for you to leave the maintenance tags (such as tidy, missinglinks, etc.) in place, to be reviewed by more experienced editors. They are better suited to judge the extent to which the page has evolved to match house style. If you feel you have read, understood and brought into practice the house style (as documented on Help:Editing and Help:Editing/House Style) on a page, you are welcome to leave a note on my or prime.movers talk page informing us about this. One of us will then check the page and judge the work that has been done, and then remove or retain the maintenance tags as appropriate. In this way, we are ensured that the site maintains maximal consistency in style, presentation, links, and most importantly, rigour. Thanks for your anticipated cooperation. --Lord_Farin (talk) 15:50, 29 December 2012 (UTC)
- Thanks for your advices! I think I understood the House Style and in fact it was the thing which made me join ProofWiki (I didn't knew the name but observed this clarity of presentation on the site). From time to time I'll probably forget about one of your formatting rules as for I'm newbie here—please be patient! :) Tell me which tag I should take preference in? Bests, joel talk 16:16, 29 December 2012 (UTC)
- The MissingLinks template is one of the most important; you can resolve this tag by connecting a page with other PW pages via internal links. This ensures that the site is comfortable to navigate, and allows readers to easily look up a certain invoked definition or theorem. As for now, I think it's best that you simply look at what changes are made to pages you have contributed to, and try to learn what the intended structures and moulds are.
- On a side note, it is most convenient to reply to a comment on a talk page directly below it. This makes the discussion much easier to follow for all contributors and others that may be interested. Hence I moved your reply back to this page. Happy editing :). --Lord_Farin (talk) 16:26, 29 December 2012 (UTC)
Amendment of pages to change notation
I see you self-reverted the changes you made on Definition:Group Direct Product, which is good.
As a general rule, unless on a specific task to ensure that the notation on the website is completely consistent (a task which is ongoing and under way by the "maintenance team"), it is normally not a constructive exercise to just change notation like that. If you feel strongly enough that the choice of symbols is poor on any given page, then feel free to raise the subject in the talk page for that page.
There is plenty of work to be done, and arbitrarily changing notation is makework. Besides, there is also often a reason (sometimes only aesthetic) for the use of the existing notation. --prime mover (talk) 17:28, 29 December 2012 (UTC)
- I get the impression that you have not taken these comments on board. Please, until you've conquered your position among the "maintenance team" cq. main contributing force, suffice to note any ideas as to page naming, operation symbols etc. on talk pages. That way, more people can give their opinion and reasons (which, contrary to popular belief, are sometimes valid and constructive). Thanks for anticipated cooperation. --Lord_Farin (talk) 23:23, 9 January 2013 (UTC)
- You also may prevent me and prime.mover from getting annoyed and preoccupied with any suggestions from your side if you do so. This makes all our lives easier, and hopefully is beneficial for website quality. --Lord_Farin (talk) 23:26, 9 January 2013 (UTC)