Page "Commutative ring" Paragraph 3

A ring is a set R equipped with two binary operations, i. e. operations combining any two elements of the ring to a third.

They are called addition and multiplication and commonly denoted by "+" and "⋅"; e. g. a + b and a ⋅ b. To form a ring these two operations have to satisfy a number of properties: the ring has to be an abelian group under addition as well as a monoid under multiplication, where multiplication distributes over addition ; i. e., a ⋅ ( b + c )