We describe the class L(R) of all left modules over a ring R such that for any matrix D over R and any solvable system of equations Fη↓ = γ↓ over a module from L(R) the system of
equations Aξ↓ = β↓ is its D-implication if and only if T(F, γ↓) = (AD,β↓) for some matrix T .
If R is a quasi-Frobenius ring, then L(R) contains the subclass of all faithful R-modules. A criterion for a system of equations over a module from L(R) to be definite is obtained.
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