JournalsrmiVol. 19, No. 2pp. 483–508

Integral Closure of Monomial Ideals on Regular Sequences

  • Karlheinz Kiyek

    Universität Paderborn, Germany
  • Jürgen Stückrad

    Universität Leipzig, Germany
Integral Closure of Monomial Ideals on Regular Sequences cover
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Abstract

It is well known that the integral closure of a monomial ideal in a polynomial ring in a finite number of indeterminates over a field is a monomial ideal, again. Let RR be a noetherian ring, and let (x1,,xd)(x_1,\ldots,x_d) be a regular sequence in RR which is contained in the Jacobson radical of RR. An ideal a\mathfrak a of RR is called a monomial ideal with respect to (x1,,xd)(x_1,\ldots,x_d) if it can be generated by monomials x1i1xdidx_1^{i_1}\cdots x_d^{i_d}. If x1R++xdRx_1R+\cdots + x_dR is a radical ideal of RR, then we show that the integral closure of a monomial ideal of RR is monomial, again. This result holds, in particular, for a regular local ring if (x1,,xd)(x_1,\ldots,x_d) is a regular system of parameters of RR.

Cite this article

Karlheinz Kiyek, Jürgen Stückrad, Integral Closure of Monomial Ideals on Regular Sequences. Rev. Mat. Iberoam. 19 (2003), no. 2, pp. 483–508

DOI 10.4171/RMI/359