blackwiki - User contributions [en]

Template:Group-like structures

2015-07-06T10:32:38Z

178.16.8.237:

{| class="infobox" style="float:right; text-align:center"
|-
! 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]]{{ref|Alpha|α}} !! [[Associativity]] !! [[Identity element|Identity]] !! [[Inverse element|Divisibility]] !! [[Commutativity]]
|-
! [[Semicategory]]
| {{no|Unneeded}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Category (mathematics)|Category]]
| {{no|Unneeded}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Groupoid]]
| {{no|Unneeded}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Magma (algebra)|Magma]]
| {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Quasigroup]]
| {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Loop (algebra)|Loop]]
| {{yes|Required}} || {{no|Unneeded}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Semigroup]]
| {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Monoid]]
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Group (mathematics)|Group]]
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Abelian Group]]
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}}
|-
| colspan="6" | {{note|Alpha|α}}[[Closure (mathematics)|Closure]], which is used in many sources, is an equivalent axiom to totality, though defined differently.
|}
<noinclude>

[[Category:Mathematics templates|{{PAGENAME}}]]

[[fr:Modèle:StructuresSemblablesGroupes]]
[[pl:Szablon:Struktury grupopodobne]]
</noinclude>

Template:Group-like structures

2015-07-05T20:04:23Z

178.16.8.237:

{| class="infobox" style="float:right; text-align:center"
|-
! 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]]
|-
! [[Semicategory]]
| {{no|Unneeded}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Category (mathematics)|Category]]
| {{no|Unneeded}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Groupoid]]
| {{no|Unneeded}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Magma (algebra)|Magma]]
| {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Quasigroup]]
| {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Loop (algebra)|Loop]]
| {{yes|Required}} || {{no|Unneeded}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Semigroup]]
| {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Monoid]]
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Group (mathematics)|Group]]
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Abelian Group]]
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}}
|-
| colspan="6" | *[[Closure (mathematics)|Closure]], which is used in many sources, is an equivalent axiom to totality, though defined differently.
|}
<noinclude>

[[Category:Mathematics templates|{{PAGENAME}}]]

[[fr:Modèle:StructuresSemblablesGroupes]]
[[pl:Szablon:Struktury grupopodobne]]
</noinclude>

Template:Group-like structures

2015-07-05T19:42:57Z

178.16.8.237:

{| class="infobox" style="float:right; text-align:center"
|-
| style="border-bottom: 2px solid #303060; text-align:center;" colspan=6 | '''Group-like structures'''
|-
! !! [[Total Function|Totality]]* !! [[Associativity]] !! [[Identity element|Identity]] !! [[Inverse element|Divisibility]] !! [[Commutativity]]
|-
! [[Semicategory]]
| {{no|Unneeded}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Category (mathematics)|Category]]
| {{no|Unneeded}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Groupoid]]
| {{no|Unneeded}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Magma (algebra)|Magma]]
| {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Quasigroup]]
| {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Loop (algebra)|Loop]]
| {{yes|Required}} || {{no|Unneeded}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Semigroup]]
| {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Monoid]]
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Group (mathematics)|Group]]
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Abelian Group]]
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}}
|-
| colspan="6" | *[[Closure (mathematics)|Closure]], which is used in many sources, is an equivalent axiom to totality, though defined differently.
|}
<noinclude>

[[Category:Mathematics templates|{{PAGENAME}}]]

[[fr:Modèle:StructuresSemblablesGroupes]]
[[pl:Szablon:Struktury grupopodobne]]
</noinclude>

Template:Group-like structures

2015-07-05T19:42:29Z

178.16.8.237:

{| class="infobox" style="float:right; text-align:center"
|-
| style="border-bottom: 2px solid #303060; text-align:center;" colspan=6 | '''Group-like structures. The entries say whether the property is ''required''.'''
|-
! !! [[Total Function|Totality]]* !! [[Associativity]] !! [[Identity element|Identity]] !! [[Inverse element|Divisibility]] !! [[Commutativity]]
|-
! [[Semicategory]]
| {{no|Unneeded}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Category (mathematics)|Category]]
| {{no|Unneeded}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Groupoid]]
| {{no|Unneeded}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Magma (algebra)|Magma]]
| {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Quasigroup]]
| {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Loop (algebra)|Loop]]
| {{yes|Required}} || {{no|Unneeded}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Semigroup]]
| {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Monoid]]
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Group (mathematics)|Group]]
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Abelian Group]]
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}}
|-
| colspan="6" | *[[Closure (mathematics)|Closure]], which is used in many sources, is an equivalent axiom to totality, though defined differently.
|}
<noinclude>

[[Category:Mathematics templates|{{PAGENAME}}]]

[[fr:Modèle:StructuresSemblablesGroupes]]
[[pl:Szablon:Struktury grupopodobne]]
</noinclude>