Note: Ideals with linear quotients

  • Authors:

  • Ali Soleyman Jahan;Xinxian Zheng

  • Affiliations:

  • Department of Mathematics, University of Kurdistan, Sanandaj, Iran;Fachbereich Mathematik und Informatik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2010

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Abstract

We study basic properties of monomial ideals with linear quotients. It is shown that if the monomial ideal I has linear quotients, then the squarefree part of I and each component of I as well as mI have linear quotients, where m is the graded maximal ideal of the polynomial ring. As an analogy to the Rearrangement Lemma of Bjorner and Wachs we also show that for a monomial ideal with linear quotients the admissible order of the generators can be chosen degree increasingly.