Function spaces of Rees matrix semigroups (Q1954001)

For a group \(G\), denote by \(G^0\) the semigroup obtained form \(G\) by adding a zero element. Given an \(I \times J\) matrix \(P\) over \(G^0\), the Rees matrix semigroup \(\mathcal{M}^0(G,P)\) is defined as the semigroup of all matrices over \(G^0\), having at most one nonzero entry, with multiplication given by \(A*B = APB\). If \(G\) is a topological group, then one also has a topology on \(\mathcal{M}^0(G,P)\). The author characterizes various compactifications of \(\mathcal{M}^0(G,P)\) as quotients of compactifications of its extensions. Also, some compactifications of tensor products of \(\mathcal{M}^0(G,P)\) with \(G\) are described in terms of compactifications of \(\mathcal{M}^0(G,P)\).