Ritt J.F. Differential Algebra

Dover Publications Inc. , 1950. - 184 pages.Review: Published 53 years ago, this book gives an overview of an area of mathematics that has found applications in algebraic, Diophantine, and differential geometry, model theory, Painleve theory, integrable systems, automatic theorem proving, combinatorics, difference equations, and symbolic programming. It could be characterized as the study of the solutions to systems of differential equations from an algebraic point of view. These differential equations can be partial or ordinary differential equations, and can be linear or nonlinear. The book is still widely cited and can still be read profitably, despite its date of publication. The author's work was inspired by the work of the mathematicians Emily Noether and van der Waerden, and is now referred to as the Ritt theory of characteristic sets of prime differential ideals. The author's work has been developed considerably further than what he envisaged, to subfields of mathematics now known as differential algebraic geometry and differential algebraic groups.