Some Notes upon “When Does \(<{\mathbb T}>\) Equal Sat \(({\mathbb T})\)?”

  • Yongbin Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6167)


Given a regular set \(\mathbb{T}\) in K[x], Lemaire et al. in ISSAC’08 give a nice algebraic property: the regular set \(\mathbb{T}\) generates its saturated ideal if and only if it is primitive. We firstly aim at giving a more direct proof of the above result, generalizing the concept of primitivity of polynomials and regular sets and presenting a new result which is equivalent to the above property. On the other hand, based upon correcting an error of the definition of U-set in AISC’06, we further develop some geometric properties of triangular sets. To a certain extent, the relation between the primitivity of \(\mathbb{T}\) and its U-set is also revealed in this paper.


Regular sets saturated ideal weakly primitive C-primitive U-set 


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yongbin Li
    • 1
  1. 1.School of Applied MathematicUniversity of Electronic Science and Technology of ChinaChengdu, SichuanChina

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