38.19 Vector Space Functions for Algebras

A finite dimensional F-algebra A is always a finite dimensional F-vector space. Thus in GAP, an algebra is a vector space (see IsVectorSpace), and vector space functions such as Base and Dimension are applicable to algebras.

    gap> a:= UnitalAlgebra( Rationals, [ [ [ 1, 0 ], [ 0, 0 ] ] ] );
    UnitalAlgebra( Rationals, [ [ [ 1, 0 ], [ 0, 0 ] ] ] )
    gap> Dimension( a );
    2
    gap> Base( a );
    [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 0, 0 ], [ 0, 1 ] ] ] 

The vector space structure is used also by the set theoretic functions.

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