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