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 be a noetherian ring, and let be a regular sequence in which is contained in the Jacobson radical of . An ideal of is called a monomial ideal with respect to if it can be generated by monomials . If is a radical ideal of , then we show that the integral closure of a monomial ideal of is monomial, again. This result holds, in particular, for a regular local ring if is a regular system of parameters of .
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Karlheinz Kiyek, Jürgen Stückrad, Integral Closure of Monomial Ideals on Regular Sequences. Rev. Mat. Iberoam. 19 (2003), no. 2, pp. 483–508DOI 10.4171/RMI/359