Illinois Journal of Mathematics

Coefficient ideals in dimension two

A. Kohlhaas

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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.

Article information

Illinois J. Math., Volume 58, Number 4 (2014), 1041-1053.

Received: 8 November 2014
Revised: 27 March 2015
First available in Project Euclid: 6 November 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
Secondary: 13C40: Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12] 13H05: Regular local rings 05E40: Combinatorial aspects of commutative algebra


Kohlhaas, A. Coefficient ideals in dimension two. Illinois J. Math. 58 (2014), no. 4, 1041--1053. doi:10.1215/ijm/1446819300.

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