Weight Ideals Associated to Regular and Log-Linear Arrays

Abstract

Certain weight-based orders on the free associative algebra $R = k<x_1, ..., x_t >$ 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.