  This article concerns commutative algebras over a field $k$ of characteristic
zero which are finite dimensional as vectorspaces, and particularly those of
such algebras which are graded. Here the term graded is applied to
non-negatively graded algebras $A$ with $A_0$ reduced and finite dimensional.
Thus the trivial grading $A=A_0$ is only allowed if $A$ is a product of finite
field extensions of $k$. It has been conjectured (G. Corti\~nas, S. Geller, C.
Weibel; The Artinian Berger Conjecture. Math. Zeitschrift {\bf 228} 3 (1998)
569-588) that for all finite dimensional algebras $A$ which are not principal
ideal algebras (i.e. have at least one nonprincipal ideal), the following
submodule of the K\"ahler differentials is nonzero: $$\bigcap{\ker(\Omega_A
@>>>\Omega_B)}$$ Here the intersection is taken over all principal ideal
algebras $B$ and all homomorphisms $A @>>>B$. In this paper we prove that the
conjecture holds for both Gorenstein graded and standard graded algebras.

Algebraic Geometry;Commutative Algebra