User:CJKG: Difference between revisions

Revision as of 08:16, 19 July 2014

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

subquasigroup
Wall theorem (= Subquasigroup of size more than half is whole quasigroup)
Ward quasigroup
Unipotent magma
Zeropotent magma
Category:Quasigroup properties

Tools

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, idempotral, 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.

I prefer transneutral, 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 transneutral element $e$ . 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)

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	Does anybody know how such an element <math>e</math> in (II) is called? I found [[neutral element\|middle neutral element]], but I don't know if that term is standardized and generally and uniformly used. Note that such an element <math>\in Q</math> is linked to the neutral element of a certain parastrophe of <math>Q</math>, and that it is the only idempotent element of <math>Q</math>. Thus maybe - just theorizing - it could be called ''unineutral'', ''idemneutral'', ''idempotral'', ''idemunit'', ''unidentity'' [YOON-, not UN-], ''mnie'' (= '''m'''iddle '''n'''eutral '''i'''dentity '''e'''lement), ''mneutral'', ''ineutral'' or ... ''Unipotent'' does not seem to be a good solution, because unipotency is a property of a structure, not of an element.		Does anybody know how such an element <math>e</math> in (II) is called? I found [[neutral element\|middle neutral element]], but I don't know if that term is standardized and generally and uniformly used. Note that such an element <math>\in Q</math> is linked to the neutral element of a certain parastrophe of <math>Q</math>, and that it is the only idempotent element of <math>Q</math>. Thus maybe - just theorizing - it could be called ''unineutral'', ''idemneutral'', ''idempotral'', ''idemunit'', ''unidentity'' [YOON-, not UN-], ''mnie'' (= '''m'''iddle '''n'''eutral '''i'''dentity '''e'''lement), ''mneutral'', ''ineutral'' or ... ''Unipotent'' does not seem to be a good solution, because unipotency is a property of a structure, not of an element.

	I prefer ''transneutral'', because in <math>x * x = e</math> the element <math>e</math> 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 transneutral element <math>e</math>.'' Thank you very much in advance. --[[User:CJKG\|CJKG]] ([[User talk:CJKG\|talk]]) 13:19, 8 July 2014 (UTC)		I prefer ''transneutral'', because in <math>x * x = e</math>, the element <math>e</math> 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 transneutral element <math>e</math>.'' or ''A pool is a quasigroup with an exoneutral element <math>e</math>.'' Thank you very much in advance. --[[User:CJKG\|CJKG]] ([[User talk:CJKG\|talk]]) 13:19, 8 July 2014 (UTC)