User:CJKG

My name is Claus, born in 1963 at Eschweiler and now living with my wife in Köln, Germany, EU. I am a teacher for mathematics and physics at the NBBK, a commercial college for physically disabled persons. --CJKG (talk) 08:47, 2 March 2014 (UTC)

• Pronounce my first name like "clouds" without "d": http://en.wikipedia.org/wiki/Claus
• My birthplace: http://en.wikipedia.org/wiki/Eschweiler
• My place of residence: "Köln" is the German name of the city of Cologne: http://en.wikipedia.org/wiki/Cologne
• My workplace: http://de.wikipedia.org/wiki/Haus_Rheinfrieden

Contribs

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

Tools

• < math > < /math >
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Inquiry: A missing property

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

(II) A magma is termed 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 termed? I found middle neutral element and middle identity, 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 $Q$. Middle neutral or middle-neutral or middle identity does not seem to be an apt solution, because it simply does not stand in the middle like a middle-associative element does. Unipotent does not seem to be a good solution, because unipotency is a property of a structure, not of an element. In fact, like the additive identity and the multiplicate identity in a ring, it is the subtractive (right) identity of a quasigroup.

In some quasigroups, $x*x=e$ is a kind of 2. In German, the multiplicate identity is called Einselement (i. e. one-element), while the additive identity is the Nullelement (i. e. zero-element). So $x*x=e$ as a kind of 2 could be the Zweielement (i. e. two-element).

Subtractive identity seems to me a good solution, better than possible - just theorizing - unineutral, idemneutral, idempotral, idemunit, unidentity [YOON-, not UN-], mnie (= middle neutral identity element), mneutral, ineutral or or or. What about transneutral (or maybe exoneutral), because in $x*x=e$, the element $e$ is on the other side of the equals sign, and Latin trans means on the opposite side, beyond?

My aim is to express (II) as easy as (I) such as A pool is a quasigroup with a subtractive (right) identity $e$. or A pool is a quasigroup with an exoneutral element $e$. Thank you very much in advance. --CJKG (talk) 13:19, 8 July 2014 (UTC)