Difference between revisions of "Template:Group-like structures"
Jump to navigation
Jump to search
imported>Addbot m (Bot: Migrating 3 interwiki links, now provided by Wikidata on d:q6009674) |
imported>Gemisi m (Inverses are not defined in general quasigroups; there is not even an identity. But unlike a general magma, left- and right-multiplication maps are bijective) |
||
| Line 24: | Line 24: | ||
|- | |- | ||
! [[Quasigroup]] | ! [[Quasigroup]] | ||
| − | | {{yes}} || {{no}} || {{no}} || {{ | + | | {{yes}} || {{no}} || {{no}} || {{no}} || {{no}} |
|- | |- | ||
! [[Groupoid]] | ! [[Groupoid]] | ||
Revision as of 16:46, 19 August 2013
| 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 | No | 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 pl:Szablon:Struktury grupopodobne