Mutations of $\mathfrak{p}\mathfrak{e}\mathfrak{r}\mathfrak{m}$ algebras

We describe mutation elements in free $\mathfrak{p}\mathfrak{e}\mathfrak{r}\mathfrak{m}$ algebras. Moreover, we construct a base of free mutation of free $\mathfrak{p}\mathfrak{e}\mathfrak{r}\mathfrak{m}$ algebra. Using Cohn’s criterion for the specialty of algebras, we show that there is an exceptional homomorphic image of mutation of free $\mathfrak{p}\mathfrak{e}\mathfrak{r}\mathfrak{m}$ algebras.