Mathematische Zeitschrift

, Volume 288, Issue 3–4, pp 935–948 | Cite as

An effective avoidance principle for a class of ideals

  • Cleto B. Miranda-NetoEmail author


Let S be a polynomial ring over a field of characteristic zero, and let \(I\subset S\) be an ideal of intersection type assumed moreover to have no embedded primary component. Our main goal in this paper is to provide an effective sufficient condition for a given monomial prime ideal to avoid the sets of prime divisors of the powers of I, and in particular to avoid the celebrated set of asymptotic prime divisors of I, which will follow from a new and quite surprising double-colon stability property. Further, we briefly describe some other applications, e.g., on the topology of a suitable blowing-up.


Monomial ideals Powers of monomial ideals Associated prime ideals Asymptotic prime divisors 

Mathematics Subject Classification

Primary 13C13 13F20 13F55 Secondary 05E40 13A99 



The author is grateful to the referee for his/her careful reading of the manuscript, helpful comments and corrections.


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© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade Federal da ParaíbaJoão PessoaBrazil

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