Weight ideals associated to regular and log-linear arrays

Academic Article


  • Certain weight-based orders on the free associative algebra $R = k$ can be specified by $t \times \infty$ arrays whose entries come from the subring of nonnegative elements in a totally ordered field. Such an array $A$ satisfying certain additional conditions produces a partial order on $R$ which is an admissible order on the quotient $R/I_A$, where $I_A$ is a homogeneous binomial ideal called the {\em weight ideal} associated to the array and whose structure is determined entirely by $A$. This article discusses the structure of the weight ideals associated to two distinct sets of arrays whose elements define admissible orders on the associated quotient algebra.
  • Status

    Publication Date

  • 2015
  • Has Subject Area

    Published In


  • Admissible orders
  • Grobner bases
  • Noncommutative Grobner bases
  • Digital Object Identifier (doi)

    Start Page

  • 1
  • End Page

  • 15
  • Volume

  • 67