By definition, a special class is a class of prime rings which is hereditary with respect to nonzero ideals and closed under essential extensions. The special class \(\pi_R\) generated by a ring \(R\) is described by Yu. M. Ryabukhin [Mat. Issled. 48, 80-93 (1978; Zbl 0409.16007)]. The purpose of the paper under review is to give a more precise characterization of the class \(\pi_R\) when \(R\) is a PI-ring. By the Posner theorem, any prime PI-ring is an order in a matrix algebra \(Q\) over a central simple algebra. Two orders \(R_1\) and \(R_2\) in the same \(Q\) are left equivalent: \(R_1\sim_lR_2\), if there exist regular elements \(a_1,a_2\in Q\) such that \(R_2a_1\subseteq R_1\) and \(R_1a_2\subseteq R_2\). The main result of the paper is the following. If \(R\) is a prime PI-ring, then \(S\in\pi_R\) if and only if \(S\) and \(R\) are left (right) iso-equivalent, i.e. there exist isomorphic images \(\overline S\) and \(\overline R\) of \(S\) and \(R\), respectively, such that \(\overline S\sim_l\overline R\).