Difference between revisions of "Template:Group-like structures"
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imported>Wmhilton (Question the totality and closure footnote) |
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| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} | | {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} | ||
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| − | | 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> | + | | colspan="6" | <small>{{note|Alpha|α}}[[Closure (mathematics)|Closure]], which is used in many sources, is an equivalent axiom to totality, though defined differently.{{Citation needed}}</small> |
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<noinclude> | <noinclude> | ||
Revision as of 17:04, 29 January 2016
| 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 |
| ^α Closure, which is used in many sources, is an equivalent axiom to totality, though defined differently.[citation needed] | |||||
fr:Modèle:StructuresSemblablesGroupes pl:Szablon:Struktury grupopodobne