User talk:Joel

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 * --Your friendly ProofWiki WelcomeBot 13:30, 27 December 2012 (UTC)

Thanks
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.

Once again, thank you for your research :) --Jshflynn (talk) 00:39, 28 December 2012 (UTC)