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An effective characterization of complete monomial ideals in two variables. (English) Zbl 1428.13012
The author characterizes complete (integrally closed) monomial ideals in two variables over a field in two ways. First he obtains a geometric characterization using the Newton polyhedron of the given ideal \(I\). The geometric characterization is used to obtain a criterion based on linear inequalities of the exponents of the monomial generators of \(I\), thus answering a question of P. Gimenez, A. Simis, W. Vasconcelos and R. Villarreal [P. Gimenez et al., J. Commut. Algebra 8, No. 2, 207–226 (2016; Zbl 1353.13006)]. Here is a quote from this paper: “We hope that this criterion would give some hints for the study of normal monomial ideals in several variables.”
13B22 Integral closure of commutative rings and ideals
13B25 Polynomials over commutative rings
Full Text: DOI
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