n A circumscribing object, (roughly) circular and hollow, looking like an annual ring, earring, finger ring etc.
n (British) A bird band, a round piece of metal put around a bird's leg used for identification and studies of migration.
n 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.
n An exclusive group of people, usually involving some unethical or illegal practices; as a crime ring, prostitution ring, etc.
n (typography) A diacritical mark in the shape of a hollow circle placed above or under the letter; a kroužek.
n (computing theory) A hierarchical level of privilege in a computer system, usually at hardware level, used to protect data and functionality (also protection ring).
n (algebra) 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.
n (algebra) 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.