Difference between revisions of "Template:Group-like structures"
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imported>KamikazeBot m (r2.7.3) (Robot: Adding af:Sjabloon:Groepagtige strukture) |
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| − | | style="border-top: 2px solid #303060" colspan=6| '''''Note:''''' ''A quasigroup with associativity (equivalently, a semigroup with | + | | style="border-top: 2px solid #303060" colspan=6| '''''Note:''''' ''A quasigroup with associativity (equivalently, a semigroup with <br /> inverses) already has an [[identity element]], and is therefore a group.'' |
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Revision as of 15:39, 20 September 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