40.9 NullAlgebra

NullAlgebra( F )

returns a trivial algebra (that is, it contains only the zero element) over the field F. Operation for Algebras) constructs a faithful representation of the zero module.

Here we meet the strange situation that an operation algebra does not consist of matrices, since in GAP a matrix always has a positive number of rows and columns. The element of a NullAlgebra( F ) is the object EmptyMat that acts (trivially) on empty lists via right multiplication.

    gap> a:= NullAlgebra( GF(2) );
    NullAlgebra( GF(2) )
    gap> Size( a );
    1
    gap> Elements( a );
    [ EmptyMat ]
    gap> [] * EmptyMat;
    [  ]
    gap> IsAlgebra( a );
    true 

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