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Integral Closure of Monomial Ideals

Paola Lea Staglianó

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Abstract

Let R be a polynomial ring over a field K. If J is an ideal of R generated by square-free monomials, then J is integrally closed. We consider an ideal I of R not generated by square-free monomials and we compute the integral closure of I,Ī. The integral closure Ī is again a monomial ideal. Therefore, the integral closure is a new combinatoric object associated to the ideal. Since monomial ideals are associated to graphs, interactions will occur in various field: networks, transports, computer science, etc. We want to highlight these issues. [ DOI : 10.1685/CSC09305] About DOI

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What this paper is about

Let R be a polynomial ring over a field K. If J is an ideal of R generated by square-free monomials, then J is integrally closed. We consider an ideal I of R not generated by square-free monomials and we compute the integral closure of I,Ī. The integral closure Ī is again a monomial ideal. Therefore, the integral closure is a new combinatoric object associated to the ideal. Since monomial ideals are associated to graphs, interactions will occur in various field: networks, transports, computer science, etc. We want to highlight these issues. [ DOI : 10.1685/CSC09305] About DOI

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Let R be a polynomial ring over a field K. If J is an ideal of R generated by square-free monomials, then J is integrally closed. We consider an ideal I of R not generated by square-free monomials and we compute the integral closure of I,Ī. The integral closure Ī is again a monomial ideal. Therefore, the integral closure is a new combinatoric object associated to the ideal. Since monomial ideals are associated to graphs, interactions will occur in various field: networks, transports, computer science, etc. We want to highlight these issues. [ DOI : 10.1685/CSC09305] About DOI

Key concepts: Monomial, Monomial ideal, Mathematics, Closure (psychology), Ideal (ethics), Polynomial ring, Square (algebra), Field (mathematics)

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