38.16 Zero and One for Algebras

Zero( A ) :

returns the additive neutral element of the algebra A.

One( A ) :

returns the (right and left) multiplicative neutral element of the algebra A if this exists, and false otherwise. If A is a unital algebra then this element is obtained on raising Algebras and Unital Algebras).

    gap> a:= Algebra( Rationals, [ [ [ 1, 0 ], [ 0, 0 ] ] ] );
    Algebra( Rationals, [ [ [ 1, 0 ], [ 0, 0 ] ] ] )
    gap> Zero( a );
    [ [ 0, 0 ], [ 0, 0 ] ]
    gap> One( a );
    [ [ 1, 0 ], [ 0, 0 ] ]
    gap> a:= UnitalAlgebra( Rationals, [ [ [ 1, 0 ], [ 0, 0 ] ] ] );
    UnitalAlgebra( Rationals, [ [ [ 1, 0 ], [ 0, 0 ] ] ] )
    gap> Zero( a );
    [ [ 0, 0 ], [ 0, 0 ] ]
    gap> One( a );
    [ [ 1, 0 ], [ 0, 1 ] ] 

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