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arXiv · 1608.08155

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

Nguyen Tu Cuong·Pham Hung Quy
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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 unmixed local rings. In two dimensional case, we compute explicitly the limit closure of a system of parameters. Some interesting examples are given.

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Nguyen Tu Cuong, Pham Hung Quy. 2016-08-29. On the limit closure of a sequence of elements in local rings. https://arxiv.org/abs/1608.08155

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