A set$R$with two binary operations $+,\cdot:R\times R\to R$is a **ring** if the following holds:

â€‹$R,+$is a commutative group with identity $0$â€‹

â€‹$R,\cdot$is a monoid (group without the inverse axiom) with identity$1$.

Distributivity: $a(b+c)=ab+ac,(a+b)c=ac+bc$â€‹

// ideals, diff types of domains