abstract
- We complete the work done by James A. Ward in the mid-twentieth century on a system of partial differential equations that defines an algebra A {\mathbb{A}} for which this system is the generalized Cauchy-Riemann equations for the derivative introduced by Sheffers at the end of the nineteenth century with respect to A {\mathbb{A}}, which is also known as the Lorch derivative with respect to A {\mathbb{A}}, and recently simply called A {\mathbb{A}} -differentiability. We get a characterization of finite-dimensional algebras, which are associative commutative with unity.