On the limit closure of a sequence of elements in local rings

Abstract

Abstract: We present a systematic study for the limit closure $(\ underline {x})^{\ lim} $ of a sequence of elements $\ underline {x} $(eg. a system of of parameters) in a local ring. Firstly, we answer the question which elements are always contained in the limit closure of a system of parameters. Then we apply this result to give a characterization of systems of parameters which is a generalization of previous results of Dutta and Roberts in\ cite {DR} and of Fouli and Huneke in\ cite {FH}. We also prove a topological characterization of ...