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

From blackwiki
Jump to navigation Jump to search
Line 3: Line 3:
 
! style="background:#cee0f2; padding:0.2em 0.4em 0.2em; text-align:center; font-size:130%; line-height:1.2em;" colspan=6 | Group-like structures
 
! style="background:#cee0f2; padding:0.2em 0.4em 0.2em; text-align:center; font-size:130%; line-height:1.2em;" colspan=6 | Group-like structures
 
|-
 
|-
! !! [[Total Function|Totality]]* !! [[Associativity]] !! [[Identity element|Identity]] !! [[Inverse element|Divisibility]] !! [[Commutativity]]
+
! !! [[Total Function|Totality]]{{ref|Alpha|α}} !! [[Associativity]] !! [[Identity element|Identity]] !! [[Inverse element|Divisibility]] !! [[Commutativity]]
 
|-
 
|-
 
! [[Semicategory]]
 
! [[Semicategory]]
Line 35: Line 35:
 
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}}
 
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}}
 
|-
 
|-
| colspan="6" | <small>*[[Closure (mathematics)|Closure]], which is used in many sources, is an equivalent axiom to totality, though defined differently.</small>
+
| colspan="6" | <small>{{note|Alpha|α}}[[Closure (mathematics)|Closure]], which is used in many sources, is an equivalent axiom to totality, though defined differently.</small>
 
|}
 
|}
 
<noinclude>
 
<noinclude>

Revision as of 10:32, 6 July 2015

Group-like structures
Totalityα Associativity Identity Divisibility Commutativity
Semicategory Unneeded Required Unneeded Unneeded Unneeded
Category Unneeded Required Required Unneeded Unneeded
Groupoid Unneeded Required Required Required Unneeded
Magma Required Unneeded Unneeded Unneeded Unneeded
Quasigroup Required Unneeded Unneeded Required Unneeded
Loop Required Unneeded Required Required Unneeded
Semigroup Required Required Unneeded Unneeded Unneeded
Monoid Required Required Required Unneeded Unneeded
Group Required Required Required Required Unneeded
Abelian Group Required Required Required Required Required
Closure, which is used in many sources, is an equivalent axiom to totality, though defined differently.

fr:Modèle:StructuresSemblablesGroupes pl:Szablon:Struktury grupopodobne