Journal of Pure and Applied Algebra vol:217 issue:2 pages:238-246
Let I be a complete M-primary ideal in a two-dimensional regular local ring (R,M) with an algebraically closed residue field. Let v_1,...,v_n denote the Rees valuations of I. In the theory of degree functions Rees and Sharp have associated with I positive integers d(I,v_1),...,d(I,v_n) providing useful information about I. We have called these integers the degree function coefficients of I. Using Zariski’s theory of complete ideals in a two-dimensional regular local ring and recent work of Heinzer and Kim on complete ideals, we obtain new interpretations of the degree function coefficients of I. Some applications are given.