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Ideals with linear quotients. (English) Zbl 1230.13016

Summary: 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 \(\mathfrak m I\) have linear quotients, where \(\mathfrak m\) 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.

MSC:

13F20 Polynomial rings and ideals; rings of integer-valued polynomials
13F55 Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes
05E45 Combinatorial aspects of simplicial complexes
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References:

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