  We demonstrate a method of associating the principal symbol at a $K$-point
with a linear differential operator acting between modules over a commutative
algebra, and we use it to define the ellipticity of a linear differential
operator in a purely algebraic way. We prove that the ellipticity is preserved
by a surjective homomorphism of algebras. As an example, we show that for every
real affine variety there is an elliptic linear differential operator acting on
the algebra of regular functions on this variety.
