User:CJKG: Difference between revisions

Revision as of 13:19, 8 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

< math > < /math >

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)

@@ Line 11: / Line 11: @@
 == Tools ==
 * [https://www.artofproblemsolving.com/Wiki/index.php/LaTeX:Symbols < math > < /math >]
+== A missing property ==
+(I)  A [[loop]] is a quasigroup with a neutral element <math>e</math>.
+(II) A magma is called [[unipotent magma|unipotent]] iff there is an element <math>e</math> such that <math>x * x = e</math> for all elements <math>x</math>.
+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'', ''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. My aim is to express (II) as easy as (I) such as ''A pool is a quasigroup with an idemneutral element <math>e</math>.'' Thank you very much in advance. --[[User:CJKG|CJKG]] ([[User talk:CJKG|talk]]) 13:19, 8 July 2014 (UTC)