Difference between revisions of "Template:Group-like structures"
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imported>R160K (Footnote was not displaying properly in pages in which this infobox was used, so incorporated it into the table) |
imported>R160K (Changed the colspan of "Group-like structures" from 5 to 6 so that it stretch over the "Commutativity" column as well) |
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| − | | style="border-bottom: 2px solid #303060" colspan= | + | | style="border-bottom: 2px solid #303060" colspan=6| '''Group-like structures''' |
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! !! [[Total Function|Totality]]* !! [[Associativity]] !! [[Identity element|Identity]] !! [[Inverse element|Inverses]] !! [[Commutativity]] | ! !! [[Total Function|Totality]]* !! [[Associativity]] !! [[Identity element|Identity]] !! [[Inverse element|Inverses]] !! [[Commutativity]] | ||
Revision as of 16:40, 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