2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165195Let $n$ be a positive integer, and let $k$ be a field (of arbitrary characteristic) accessible to symbolic computation. We describe an algorithmic test for determining whether or not a finitely presented $k$-algebra $R$ has infinitely many equivalence classes of semisimple representations $R \to M_n(k')$, where $k'$ is the algebraic closure of $k$. The test reduces the problem to computational commutative algebra over $k$, via famous results of Artin, Procesi, and Shirshov. The test is illustrated by explicit examples, with $n = 3$.12 pages, no figures. Revised; to appear in Journal of Algebra (Computational Section)Rings and AlgebrasCommutative Algebra16Z05 (Primary); 16R30, 13P10 (Secondary)text