  A Gorenstein A-algebra R of codimension 2 is a perfect finite A-algebra such
that R=Ext^2(R,A) holds as R-modules, A being a Cohen-Macaulay local ring with
dim(A)-dim_A(R)=2. I prove a structure theorem for these algebras improving on
an old theorem of M. Grassi. Special attention is paid to the question how the
ring structure of R is encoded in its Hilbert resolution. It is shown that R is
automatically a ring once one imposes a weak depth condition on a determinantal
ideal derived from a presentation matrix of R over A. The interplay of
Gorenstein algebras and Koszul modules as introduced by M. Grassi is clarified.
Questions of applicability to canonical surfaces in P^4 have served as a
guideline in these investigations.
