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| style="border-bottom: 2px solid #303060" colspan=11| '''Ring-like structures'''
|-
! !! [[Magma]]* !! [[Semigroup]] !! [[Monoid]] !! [[Commutative monoid]] || [[Group]] !! [[Abelian Group]] !! [[Loop]] !! [[Quasigroup]] !! [[Groupoid]] !! [[Cathegory]] !! [[Semicathegory]]
|-
! [[Magma (algebra)|Magma]]
| Y || N || N || ? || N || N || N || N || N || N || N
|-
! [[Semigroup]]
| Y || N || N || ? || N || N || N || N || N || N || N
|-
! [[Monoid]]
| Y || N || N || ? || N || N || N || N || N || N || N|-! [[Monoid|Commutative monoid]]| ? || ? || ? || ? || ? || ? || ? || ? || ? || ? || ?
|-
! [[Group (mathematics)|Group]]
| Y || N || N || ? || N || N || N || N || N || N || N
|-
! [[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
|}
