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→Ring-like structures
== Group-like structures ==
Taken from [http://en.wikipedia.org/wiki/Template:Group-like_structures]
{| style="text-align:center"
! [[Monoid]]
| Y || Y || Y || N || N
|-
! [[Monoid|Commutative monoid]]
| Y || Y || Y || N || Y
|-
! [[Group (mathematics)|Group]]
|}
== Ring-like structures ==
{| style="text-align:center"
|- align="center"
| style="border-bottom: 2px solid #303060" colspan=117| '''Ring-like structures'''
|-
! !! [[Magma]]* !! [[Semigroup]] !! [[MonoidCommutative semigroup]] !! [[GroupMonoid]] !! [[Abelian GroupCommutative monoid]] !! || [[LoopGroup]] !! [[Quasigroup]] !! [[Groupoid]] !! [[Cathegory]] !! [[SemicathegoryAbelian Group]]
|-
! [[Magma (algebra)|Magma]]
| Y [http://www.proofwiki.org/wiki/Definition:Ringoid Ringoid] || N ? || N ? || N ? || N ? || N ? || N || N || N || N?
|-
! [[Semigroup]]
| Y ? || N [http://www.proofwiki.org/wiki/Definition:Semiring_%28Abstract_Algebra%29 Semiring] || N ? || N ? || N ? || N ? || N ?|-! [[Commutative semigroup]]| N ? || N [http://www.proofwiki.org/wiki/Definition:Additive_Semiring Additive semiring, semiring] || N? || ? || ? || ? || ?
|-
! [[Monoid]]
| Y ? || N [http://www.proofwiki.org/wiki/Definition:Rig Rig, semiring] || N ? || N ? || N ? || N ? || N ?|-! [[Monoid| N Commutative monoid]]|? | N |[http://www.proofwiki.org/wiki/Definition:Rig Rig] | N| ? || ? || ? || ? || ?
|-
! [[Group (mathematics)|Group]]
| Y ? || N ? || N ? || N ? || N ? || N ? || N || N || N || N?
|-
! [[Abelian Group]]
| Y ? || N || N || N || N || N || N || N || N || N|-! [[Loop (algebra)|Loop]http://en.wikipedia.org/wiki/Ring_%28mathematics%29 Ring]| Y |? | N || N || N || N || N || N || N || N || N|-! [[Quasigroup]http://en.wikipedia.org/wiki/Ring_%28mathematics%29 Unital ring]| Y || N || N || N || N || N || N || N || N || N|-! [[Groupoid]http://en.wikipedia.org/wiki/Commutative_ring Commutative ring]| Y || N || N || N || N || N || N || N || N || N|-! [[Category http://mathworld.wolfram.com/DivisionAlgebra.html Division ring (mathematicsalgebra)|Category]]| Y || N || N || N || N || N || N || N || N || N|-! [[Semicategory]http://en.wikipedia.org/wiki/Field_%28mathematics%29 Field]| Y || N || N || N || N || N || N || N || N || N
|}
