Add to ORKGLet $f\sb1,\... ,f\sb{d}$ be elements generating an ideal primary to a maximal ideal in a commutative Noetherian ring R. Let K = R/m be the residue field. The thesis studies the behavior of the K-vector space dimension of the socle of $R\sb{N} = R/(f\sbsp{1}{N},\... ,f\sbsp{d}{N})$ as a function of N. The socle in this case is the same as Ann$\sb{R\sb{n}} (m)$. This function is related in spirit to the Hilbert-Kunz and Hilbert-Samuel functions. It is shown here that the function described is bounded above by a constant times $N\sp{{\rm dim}(R)-2}$. We also show that dim$({\it R\/})-2$ is the smallest possible degree on N for an upper bound in this generality. Even when bounded, this function need not be periodic. We give a family of example...
