Difference between revisions of "Template:Group-like structures"
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imported>Eric Kvaalen (The entries say whether the property is required.) |
(Shrank footnote so the table as a whole isn't as wide.) |
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| {{no}} || {{yes}} || {{no}} || {{no}} || {{no}} | | {{no}} || {{yes}} || {{no}} || {{no}} || {{no}} | ||
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− | + | | colspan="6" | <small>*[[Closure (mathematics)|Closure]], which is used in many sources, is an equivalent axiom to totality, though defined differently.</small> | |
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Revision as of 15:26, 12 November 2014
Group-like structures. The entries say whether the property is required. | |||||
Totality* | Associativity | Identity | Divisibility | 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, is an equivalent axiom to totality, though defined differently. |
fr:Modèle:StructuresSemblablesGroupes pl:Szablon:Struktury grupopodobne