On the symmetric algebra of an ideal

The symmetric algebra of an ideal I may be compared to the Rees algebra via the canonical epimorphism :Sym(I)R(I). A necessary and sufficient criterion is given for a to be an isomorphism, and sequential conditions on the symmetric algebra are studied. Some applications are given to Proj :ProjR(I)Pro'j Sym(I) and to the theory of approximation complexes.The material presented in this paper constitutes part of the author's thesis submitted to Universität Essen