Abstract
The construction of Arf rings and strictly closed rings has been studied widely; however, there has been no clear description of the structure of the strict closure R⁎ when R‾ is not a finitely generated R-module. In this paper, we investigate the construction and finite generation of the strict closure of rings. We determine its structure when R is a Cohen-Macaulay semi-local ring of dimension one, with dimRM=1 for every M∈MaxR. Using this, a characterization of the finite generation of the strict closure is given.
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