This article is about a mathematical concept , for the piece of jewellery , see ring In mathematics , a ring is an algebraic structure consisting of a set together with 2 operations : addition ( + ) and multiplication ( â cents ) . In mathematics , a ring is an algebraic structure consisting of a set together with two binary operations usually called addition and multiplication , where the set is an abelian group under addition ( called the additive group of the ring ) and a monoid under multiplication such that multiplication distributes over addition .