# Introduction

Matrix algebras (or matrix rings) may be defined over any ring $S$. We shall regard such a matrix algebra as an $S$*-algebra*. Let us denote the complete algebra of $n\times n$ matrices over $S$ by $M_n(S)$. It will often be convenient to regard $M_n(S)$ as the endomorphism ring of the free $S$-module $S^{(n)}$. We will then speak of $S^{(n)}$ as the natural $S$-module associated with $M_n(S)$.

Matrix algebras have type `AlgMat` and their elements have type `AlgMatElt`. These types inherit from `AlgMatV` and `AlgMatVElt` respectively (which cover both ordinary matrix algebras and matrix Lie algebras).