Introduction

A structure constant algebra \(A\) of dimension \(n\) over a ring \(R\) can be defined in Magma by giving the \(n^3\) structure constants \(a_{ij}^k \in R ( 1 \le i, j, k \le n)\) such that, if \({e_1, e_2, \ldots, e_n}\) is the basis of \(A\), \(e_i * e_j = \sum_{k = 1}^n a_{ij}^k * e_k.\) Structure constant algebras may be defined over any unital ring \(R\). However, many operations require that \(R\) be a Euclidean domain or even a field.