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Rings
A set
$R$
with two binary operations
$+,\cdot:R\times R\to R$
is a ring if the following holds:
$R,+$
is a commutative group with identity
$0$
$R,\cdot$
is a monoid (group without the inverse axiom) with identity
$1$
.
Distributivity:
$a(b+c)=ab+ac,(a+b)c=ac+bc$
// ideals, diff types of domains