%0 Journal Article
%A Pogorui, A. A.
%A Rodríguez-Dagnіno, Ramón М.
%A Shapіro, Мichael
%D 2013
%F zu2:13298
%I John Wiley & Sons
%J Math. Meth. Appl. Sci.
%T Solutions for PDEs with constant coefficients and derivability of functions ranged in commutative algebras
%U http://eprints.zu.edu.ua/13298/
%X It is well known that the real and imaginary parts of any holomorphic function are harmonic functions of two variables. In this paper,  we extend this idea to finite-dimensional commutative algebras; that is, we prove that if some basis of a subspace of a commutative  algebra satisfies a polynomial equation, then the components of a monogenic function on the subspace are solutions of the respective  partial differential equation (PDE). We illustrate these concepts with a few examples.