An algebra that synthesizes relational query concepts with object-oriented databases is defined. The algebra fully supports abstract data types and object identity, while providing associative access to objects. The operations take an abstract view of objects and access typed collections of objects through the public interface defined for the type. The algebra supports access to relationships implied by the structure of the objects, as well as the definition and creation of new relationships between objects. The operations create new objects with unique identities and can use object identity in the manipulation of objects. The support for object identity leads to new definitions for equality of results and operators that can manipulate the identities of objects.>