Weight Ideals Associated to Regular and Log-Linear Arrays

Details Weight Ideals Associated to Regular and Log-Linear Arrays Weight Ideals Associated to Regular and Log-Linear Arrays

2011-01-31

arxiv.org/abs/1101.6004v1

Mathematics

Rings and Algebras

22 pages

Scientific paper

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.

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