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]] !! [[Quasigroup|Divisibility]] !! [[Commutativity]]
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! !! [[Total Function|Totality]]* !! [[Associativity]] !! [[Identity element|Identity]] !! [[Inverse element|Divisibility]] !! [[Commutativity]]
 
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! [[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