| Abstrakt: |
Let ( R;m) be a 2-dimensional rational singularity with algebraically closed residue field and whose associated graded ring is an integrally closed domain. Göhner has shown that for every prime divisor v of R, there exists a unique one-fibered complete m-primary ideal A in R with unique Rees valuation v and such that any complete m-primary ideal with unique Rees valuation v, is a power of A. We show that for v ≠ ord, A is the inverse transform of a simple complete ideal in an immediate quadratic transform of R, if and only if the degree coefficient d( A; v) is 1. We then give a criterion for R to be regular. [ABSTRACT FROM AUTHOR] |
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