Symmetries of Diﬀerential Ideals and Diﬀerential Equations
Thepaperdeals with diﬀerential rings andpartial diﬀerentialequations withcoeﬃcientsin some algebra. We introduce symmetries and the conservation laws to the diﬀerential ideal of an arbitrary diﬀerential ring. We prove that a set of symmetries of an ideal forms a Lie ring and give a precise criterion when a diﬀerentiationisa symmetryofanideal. Theseconceptsare applied topartial diﬀerentialequations.