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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]]
|-
| || colspan="5" | <small>**Each element of a [[Loop (algebra)|loop]] has a left and right inverse, but these need not coincide.</small>
|}
== Ring-like structures ==
{| style="text-align:center"
|- align="center"
| style="border-bottom: 2px solid #303060" colspan=7| '''Ring-like structures'''
|-
! !! [[Magma]]* !! [[Semigroup]] !! [[Commutative semigroup]] !! [[Monoid]] !! [[Commutative monoid]] || [[Group]] !! [[Abelian Group]]
|-
! [[Magma (algebra)|Magma]]
| [http://www.proofwiki.org/wiki/Definition:Ringoid Ringoid] || ? || ? || ? || ? || ? || ?
|-
! [[Semigroup]]
| ? || [http://www.proofwiki.org/wiki/Definition:Semiring_%28Abstract_Algebra%29 Semiring] || ? || ? || ? || ? || ?
|-
! [[Commutative semigroup]]
| ? || [http://www.proofwiki.org/wiki/Definition:Additive_Semiring Additive semiring, semiring] || ? || ? || ? || ? || ?
|-
! [[Monoid]]
| ? || [http://www.proofwiki.org/wiki/Definition:Rig Rig, semiring] || ? || ? || ? || ? || ?
|-
! [[Monoid|Commutative monoid]]
| ? || [http://www.proofwiki.org/wiki/Definition:Rig Rig] || ? || ? || ? || ? || ?
|-
! [[Group (mathematics)|Group]]
| ? || ? || ? || ? || ? || ? || ?
|-
! [[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]
|}
