Additive Subgroup

A subset of a Ring $R$ that has:

• Closure Under Addition ($\forall a,b\in S,a+b\in S$)
• Additive Identity ($0_R\in S$)
• Additive Inverse ($\forall a\in S,\exists -a\in S\text{ s.t }a{+}_R(-a)=0$)