Difference between revisions of "Template:Group-like structures"
Jump to navigation
Jump to search
imported>Eric Kvaalen (The entries say whether the property is required.) |
(Shrank footnote so the table as a whole isn't as wide.) |
||
| Line 35: | Line 35: | ||
| {{no}} || {{yes}} || {{no}} || {{no}} || {{no}} | | {{no}} || {{yes}} || {{no}} || {{no}} || {{no}} | ||
|- | |- | ||
| − | + | | colspan="6" | <small>*[[Closure (mathematics)|Closure]], which is used in many sources, is an equivalent axiom to totality, though defined differently.</small> | |
|} | |} | ||
<noinclude> | <noinclude> | ||
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