38.10 IsSubalgebra

IsSubalgebra( A, U )

returns true if U is a subalgebra of A and false otherwise.

Note that A and U must have a common parent algebra. This function returns true if and only if the set of elements of U is a subset of the set of elements of A.

    gap> a:= [ [ 1, 0 ], [ 0, 0 ] ];;
    gap> b:= [ [ 0, 0 ], [ 0, 1 ] ] ;;
    gap> alg:= Algebra( Rationals, [ a, b ] );;
    gap> alg.name:= "alg";;
    gap> IsSubalgebra( alg, alg );
    true
    gap> s:= UnitalSubalgebra( alg, [ a ] );
    UnitalSubalgebra( alg, [ [ [ 1, 0 ], [ 0, 0 ] ] ] )
    gap> IsSubalgebra( alg, s );
    true 

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