Module isomorphism

A module isomorphism is a bijection of modules over the same ring preserving addition and scalar multiplication. Its inverse preserves these operations too. When a linear operator $T$ gives a vector space an $F[t]$-module structure by $t\cdot v=T(v)$, a module isomorphism is exactly an invertible linear map intertwining the two operators. This translates classification of modules into matrix similarity and rational canonical form.