MAGMA Computational Algebra System

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 x 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⁾. We will then speak of S⁾ 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).