This paper approaches the incremental view maintenance problem from an algebraic perspective. We construct a ring of databases and use it as the foundation of the design of a query calculus that allows to express powerful aggregate queries. The query calculus inherits key properties of the ring, such as having a normal form of polynomials and being closed under computing inverses and delta queries. The k-th delta of a polynomial query of degree k without nesting is purely a function of the update, not of the database. This gives rise to a method of eliminating expensive query operators such as joins from programs that perform incremental view maintenance. The main result is that, for non-nested queries, each individual aggregate value can be incrementally maintained using a constant amount of work. This is not possible for nonincremental evaluation.