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Although many data manipulation languages (DML's) have been proposed for the entity-relationship (ER) model, there is no agreement on what are the basic manipulations that any ER DML must offer. Moreover, there is no DML which fully supports all the capabilities of a general ER model with n-ary relationships, relationships with attributes, optional, complex, and multivalued attributes. This paper consequently proposes a definition of a set of algebraic operators to be applied on a general ER database. The algebra is said to be complete through equivalence with the usual definition of completeness for relational data manipulation languages. This work is intended to provide a sound basis for the definition of complete entity-relationship DML's, an essential feature to make the ER model fully operational.