Abstract
We describe coefficient ideals for both $(x,y)$-primary monomial ideals in $k[x,y]$ and $\mathfrak{m}$-primary ideals in two-dimensio-nal regular local rings $(R,\mathfrak{m})$ by linking them to certain ideals of reduction number one. In the monomial case, we then explicitly determine the generators of a coefficient ideal by showing their symmetric relationship to the generators of the associated reduction number one ideal.
Citation
A. Kohlhaas. "Coefficient ideals in dimension two." Illinois J. Math. 58 (4) 1041 - 1053, Winter 2014. https://doi.org/10.1215/ijm/1446819300
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