The operators of the relational algebra were already described in Codd’s pioneering paper . In  he introduced the term relational algebra and showed its equivalence with the tuple relational calculus.
This entry details the definition of the relational algebra in the unnamed perspective , with selection, projection, cartesian product, union and difference operators. It also describes some operators of the named perspective  such as join.
The flagship property of the relational algebra is that it is equivalent to the (undecidable!) set of domain independent relational calculus queries thus providing a standard for relational completeness.
Fix a countably infinite set ⅅ of constants over which Σ-instances are defined for a relational schema Σ.
The relational algebra is a many-sorted algebra, where the sorts are the natural numbers. The idea is that the elements of sort n are finite n-ary relations. The carrier of sort nof the algebra is the set of...
- 1.Abiteboul S, Hull R, Vianu V. Foundations of databases: the logical level. Reading: Addison Wesley; 1994.Google Scholar
- 3.Codd EF. Relational completeness of database sublanguages. In: Rustin R, editor. Courant computer science symposium 6: data base systems. Englewood Cliffs: Prentice-Hall; 1972. p. 65–98.Google Scholar