Difference between revisions of "Template:Group-like structures"
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imported>LokiClock (Defeats the purpose of the table, which is to classify the structures by their identities, visibly on inspection.) |
imported>LokiClock (better link) |
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| style="border-bottom: 2px solid #303060" colspan=6| '''Group-like structures''' | | style="border-bottom: 2px solid #303060" colspan=6| '''Group-like structures''' | ||
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− | ! !! [[Total Function|Totality]]* !! [[Associativity]] !! [[Identity element|Identity]] !! [[ | + | ! !! [[Total Function|Totality]]* !! [[Associativity]] !! [[Identity element|Identity]] !! [[Inverse element|Divisibility]] !! [[Commutativity]] |
|- | |- | ||
! [[Magma (algebra)|Magma]] | ! [[Magma (algebra)|Magma]] |
Revision as of 11:19, 22 March 2014
Group-like structures | |||||
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 to define group-like structures, is an equivalent axiom to totality, though defined differently. |
fr:Modèle:StructuresSemblablesGroupes pl:Szablon:Struktury grupopodobne