In this paper, the authors approach the incremental view maintenance problem from an algebraic perspective. The algebraic structure of a ring of databases is constructed and extended to form a powerful aggregate query calculus. The query calculus inherits the key properties of rings, such as distributive and the existence of an additive inverse. As a consequence, the calculus has a normal form of polynomials and is closed under a universal difference operator. This difference operator allows to express the so-called delta queries of the incremental view maintenance literature, but also deltas to the deltas (second deltas), deltas to second deltas (third deltas), and so on.