 We say that \(\mathcal{A}^{\prime }\) is a substructure of \(\mathcal{A}\) (equivalently, \(\mathcal{A}\) is an extension of \(\mathcal{A}^{\prime }\)) if and only if the inclusion map \(i\) (sending every element to itself) is an embedding from \(\mathcal{A}^{\prime }\) to \(\mathcal{A}\).