A place where some sports or exhibitions take place; notably a circular or comparable arena, such as a boxing ring or a circus ring; hence the field of a political contest.
An algebraic structure which consists of a set with two binary operations: an additive operation and a multiplicative operation, such that the set is an abelian group under the additive operation, a monoid under the multiplicative operation, and such that the multiplicative operation is distributive with respect to the additive operation.
An algebraic structure as above, but only required to be a semigroup under the multiplicative operation, that is, there need not be a multiplicative identity element.