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Jahan, Ali Soleyman; Zheng, Xinxian
Journal of combinatorial theory. Series A, 2010, 2010-01-00, Volume: 117, Issue: 1Journal Article
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 m I have linear quotients, where m is the graded maximal ideal of the polynomial ring. As an analogy to the Rearrangement Lemma of Björner and Wachs we also show that for a monomial ideal with linear quotients the admissible order of the generators can be chosen degree increasingly.
