User:CJKG

My name is Claus [pronounce like "clouds" without d], born in 1963, living in Köln [Cologne], Germany, EU. I am a maths teacher. --CJKG (talk) 08:47, 2 March 2014 (UTC)

My contributions

1. subquasigroup
2. Wall theorem (= Subquasigroup of size more than half is whole quasigroup)
3. Ward quasigroup
4. Unipotent magma
5. Zeropotent magma
6. Category:Quasigroup properties

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A missing property

(I) A loop is a quasigroup with a neutral element $e$.

(II) A magma is called unipotent iff there is an element $e$ such that $x*x=e$ for all elements $x$.

Does anybody know how such an element $e$ in (II) is called? I found middle neutral element, but I don't know if that term is standardized and generally and uniformly used. Note that such an element $\in Q$ is linked to the neutral element of a certain parastrophe of $Q$, and that it is the only idempotent element of $Q$. Thus maybe - just theorizing - it could be called unineutral, idemneutral, idemunit, unidentity [YOON-, not UN-], mnie (= middle neutral identity element), mneutral, ineutral or ... Unipotent does not seem to be a good solution, because unipotency is a property of a structure, not of an element. My aim is to express (II) as easy as (I) such as A pool is a quasigroup with an idemneutral element $e$. Thank you very much in advance. --CJKG (talk) 13:19, 8 July 2014 (UTC)