Presentations of Munn matrix algebras over \(K\)-algebras with \(K\) being a commutative ring

Abstract

We consider the Munn matrix algebras over an associative unital \(K\)-algebra \(\mathcal{A}\), where \(K\) is a commutative (unital) ring and \(\mathcal{A}\) as a \(K\)-module is free (of finite or infinite rank), and, for each (not necessarily finitely defined) presentation of \(\mathcal{A}\), we give presentations of the Munn matrix algebras over it.