Some remarks on Kنhler differentials and ordinary differentials in nonlinear control theory

In the algebraic approach to nonlinear control systems two similar notions, namely Kنhler differentials and the formal vector space of differential one-forms having the properties of ordinary differentials, are frequently used to study the systems. This technical note explains that the formal vector space of differential one-forms is isomorphic to a quotient space (module) of Kنhler differentials. These two modules coincide when they are modules over a ring of linear differential operators over the field of algebraic functions. Some remarks and examples demonstrating when the use of Kنhler differentials might not be appropriate are included.