Abstract
ABSTRACTA local ring is called a local ring of simple singularity of dimension one over the real field if it is isomorphic to a ring of the form ℝ{x,y}∕(f) and the number of proper ideals I of ℝ{x,y} with f∈I2 is finite. We first give a complete classification of local rings of simple singularity of dimension one over the real field. We also show that the rings have an infinitely generated prime cone unless they are isomorphic to either or , where n is a positive integer.
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