An introduction to differential algebra. (English) Zbl 0083.03301

Actualités Scientifiques et Industrielles. 1251. Publ. Inst. Math. Univ. Nancago. V. Paris: Hermann & Cie. 62 p. (1957).
As the author states in the preface, this small book on differential algebra is an effort toward making “the subject more easily accessible to the mathematical community”. The reader with a reasonable background in ordinary algebra plus some elementary point-set topology will find this book a clear and concise, self-contained introduction to the basic works of Ritt on differential algebra, to those of Kolchin on the Picard-Vessiot theory and Galois theory of differential fields, and to the theory of algebraic matrix groups.
Probably the only criticism has to do with the numerous typographical errors in the proofs of various theorems; the inclusion of a list of errata would not be out of order. However, the statements of the theorems seem generally to be free of errors. Aside from these relatively minor objections the book certainly achieves its purpose and can be easily recommended.


12H05 Differential algebra
12-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory