Abelian Group is a #Group which also satisfies the following property:
- Communicative of addition, which means \(\forall a, b \in S, a + b = b + a\).
Abelian Group
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Ring
Ring is a Set# \(R\), together with two operations \(+\) and \(*\), which has the following properties including those in #Group and #Abelian Group:
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Integral Domain
Integral Domain is a #Ring which satisfies the following properties including those in #Group, #Abelian Group and #Communicative Ring.
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Group
If the group is also commutative, then it is also an Abelian Group#.
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Field
Field is a Set# \(S\), together with two operations \(+\) and \(*\), which has the following properties including those in #Group, #Abelian Group, #Ring, #Communicative Ring, and #Integral Domain:
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Communicative Ring
Communicative Ring is a #Ring where its multiplicative operation is communicative, as shown below. It also satisfies the properties from #Group and #Abelian Group.
- Algebraic Structure