Difference between revisions of "Template:Group-like structures"
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imported>LokiClock (Show identity after totality (thematic property)) |
imported>KamikazeBot m (r2.7.3) (Robot: Adding af:Sjabloon:Groepagtige strukture) |
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[[Category:Mathematics templates|{{PAGENAME}}]] | [[Category:Mathematics templates|{{PAGENAME}}]] | ||
| + | [[af:Sjabloon:Groepagtige strukture]] | ||
[[cs:Šablona:Grupové struktury]] | [[cs:Šablona:Grupové struktury]] | ||
[[fr:Modèle:StructuresSemblablesGroupes]] | [[fr:Modèle:StructuresSemblablesGroupes]] | ||
Revision as of 11:38, 27 August 2012
| Requirements of group-like structures | |||||
| Totality | Identity | Associativity | Inverses | Commutativity | |
|---|---|---|---|---|---|
| Magma | Yes | No | No | No | No |
| Unital | Yes | Yes | No | No | No |
| Quasigroup | Yes | No | No | Yes | No |
| Loop | Yes | Yes | No | Yes | No |
| Semigroup | Yes | No | Yes | No | No |
| Monoid | Yes | Yes | Yes | No | No |
| Group | Yes | Yes | Yes | Yes | No |
| Abelian Group | Yes | Yes | Yes | Yes | Yes |
| Groupoid | No | Yes | Yes | Yes | No |
| Category | No | Yes | Yes | No | No |
| Semicategory | No | No | Yes | No | No |
| Note: A quasigroup with associativity (equivalently, a semigroup with inverses) already has an identity element, and is therefore a group. | |||||
af:Sjabloon:Groepagtige strukture cs:Šablona:Grupové struktury fr:Modèle:StructuresSemblablesGroupes ja:Template:Group-like structures pl:Szablon:Struktury grupopodobne sv:Mall:Gruppliknande strukturer zh:Template:類群結構