An additive commutative group in which a second operation (normally considered as multiplication) is also defined.

The multiplication must be associative, i.e. a+(b+c)=(a+b)+c and the distributive law a(b + c) = ab + ac and (b + c)a = ba + ca must hold.

If a ring is also a commutative multiplicative group then it′s called a field.

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Subjects: Algebra