# Relational Algebra

**DOI:**https://doi.org/10.1007/978-1-4614-8265-9_967

## Definition

The operators of the relational algebra were already described in Codd’s pioneering paper [2]. In [3] 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* [1], with selection, projection, cartesian product, union and difference operators. It also describes some operators of the *named perspective* [1] 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*.

## Key Points

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 *n*of the algebra is the set of...

## Recommended Reading

- 1.Abiteboul S, Hull R, Vianu V. Foundations of databases: the logical level. Reading: Addison Wesley; 1994.Google Scholar
- 2.Codd EF. A relational model of data for large shared data banks. Commun ACM. 1970;13(6):377–87.zbMATHCrossRefGoogle 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
- 4.Ramakrishnan R, Gehrke J. Database management systems. 3rd ed. New York: McGraw-Hill; 2003.zbMATHGoogle Scholar