#
# file:         ass.gap
# purpose:      functions for associative algberas
# created:      pasha jan 9 2005
# modified:     pasha jan 10 2005
# modification: try to handle infinite-dimensional case
#


# whether an algebra is square-zero; returns true of false
IsSquareZero := function (A)
	local B, i, j;

	if Dimension(A) < infinity then
		B := Basis(A);
	else
		# should'n we always check generators instead of basis?
		B := GeneratorsOfAlgebra (A);
	fi;

	for i in [1..Length(B)] do
    	for j in [1..Length(B)] do
        	if B[i]*B[j] <> Zero(A) then
          		return (false);
        	fi;
      	od;
    od;

    return (true);
end;


# returns square-zero algebra over a field K of dimension n
SquareZeroAlgebra := function (K, n)
	return (AlgebraByStructureConstants (K, EmptySCTable (n, Zero(K))));
end;


# end of ass.gap