Can also be called Nonadditive.
If you decompose a relation into relations and you will guarantee a Lossless-Join if ⋈ = .

Let be a relation schema.

Let be a set of functional dependencies

Functional dependency

A functional dependency is a constraint between two sets of attributes in a relation from a database.Given a relation R, a set of attributes X in R is said to functionally determine another attribute Y, also in R, if, and only if, each X value is associated with precisely one Y value...

 on .

Let and form a decomposition of .

The decomposition is a lossless-join decomposition of R if at least one of the following functional dependencies are in ⁺(where ⁺ stands for the closure for every attribute in ):

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