Difference between revisions of "Template:Group-like structures"

From blackwiki
Jump to navigation Jump to search
imported>R160K
(Added a footnote explaining the equivalence of "closure" and "totality" - there have been various edits back and forth between "closure" and "totality", although I hope nobody will object to a footnote)
imported>R160K
(Footnote was not displaying properly in pages in which this infobox was used, so incorporated it into the table)
Line 34: Line 34:
 
! [[Semicategory]]
 
! [[Semicategory]]
 
| {{no}} || {{yes}} || {{no}} || {{no}} || {{no}}
 
| {{no}} || {{yes}} || {{no}} || {{no}} || {{no}}
 +
|-
 +
| || colspan="5" | <small>*[[Closure (mathematics)|Closure]], which is used in many sources to define group-like structures, is an equivalent axiom to totality, though defined differently.</small>
 
|}
 
|}
<small>*[[Closure (mathematics)|Closure]], which is used in many sources to define group-like structures, is an equivalent axiom to totality, though defined differently.</small>
 
 
<noinclude>
 
<noinclude>
  

Revision as of 16:38, 4 November 2012

Group-like structures
Totality* Associativity Identity Inverses Commutativity
Magma Yes No No No No
Semigroup Yes Yes No No No
Monoid Yes Yes Yes No No
Group Yes Yes Yes Yes No
Abelian Group Yes Yes Yes Yes Yes
Loop Yes No Yes Yes No
Quasigroup Yes No No Yes No
Groupoid No Yes Yes Yes No
Category No Yes Yes No No
Semicategory No Yes No No No
*Closure, which is used in many sources to define group-like structures, is an equivalent axiom to totality, though defined differently.

fr:Modèle:StructuresSemblablesGroupes ja:Template:Group-like structures pl:Szablon:Struktury grupopodobne sv:Mall:Gruppliknande strukturer zh:Template:類群結構