Let be a commutative Noetherian ring, and let be a regular -sequence contained in the Jacobson radical of . An ideal of is said to be a monomial ideal with respect to if it is generated by a set of monomials . The monomial closure of , denoted by , is defined to be the ideal generated by the set of all monomials such that for some . It is shown that the sequences and , of associated prime ideals are increasing and ultimately constant for large . In addition, some results about the monomial ideals and their integral closures are included.
Cite this article
Monireh Sedghi, Asymptotic behaviour of monomial ideals on regular sequences. Rev. Mat. Iberoam. 22 (2006), no. 3, pp. 955–962DOI 10.4171/RMI/479