Book Review

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Book Information:

Editors: H. Bass, A. Buium and P.J. Cassidy

Title: Selected works of Ellis Kolchin

Additional book information: edited by H. Bass, A. Buium and P.J. Cassidy, American Mathematical Society, Providence, RI, 1999, xiii + 639 pp., ISBN 0-8218-0542-8, $120.00

**1.**Bertrand, D., Review of Lectures on Differential Galois Theory by A. Magid, Bull. Amer. Math. Soc., vol. 33, 1996, pp. 289-294.**2.**Borel, A., Algebraic groups and Galois theory in the work of Ellis R. Kolchin, in Selected Works of Ellis Kolchin with Commentary, eds. Bass, H., et al., American Mathematical Society, Providence, 1999, pp. 505-526. CMP**99:09****3.**Buium, A. and Cassidy, P., Differential algebraic geometry and differential algebraic groups: From algebraic differential equations to Diophantine geometry, in Selected Works of Ellis Kolchin with Commentary, eds. Bass, H., et al., American Mathematical Society, Providence, 1999, pp. 567-636. CMP**99:09****4.**P. Deligne,*Catégories tannakiennes*, The Grothendieck Festschrift, Vol. II, Progr. Math., vol. 87, Birkhäuser Boston, Boston, MA, 1990, pp. 111–195 (French). MR**1106898****5.**Janelidzhe, G., Galois theory in categories: the new example of differential fields, in Categorical Topology and Its Relation to Analysis Algebra and Combinatorics: Prague, Czechoslovakia, 22-27 August 1988, eds. Adamek, J. and Mac Lane, S., World Scientific (1989), pp. 369-380.**6.**E. R. Kolchin,*Differential algebra and algebraic groups*, Academic Press, New York-London, 1973. Pure and Applied Mathematics, Vol. 54. MR**0568864****7.**E. R. Kolchin,*Differential algebraic groups*, Pure and Applied Mathematics, vol. 114, Academic Press, Inc., Orlando, FL, 1985. MR**776230****8.**, Algebraic matric groups and the Picard-Vessiot theory of homogeneous ordinary differential equations, in Selected Works of Ellis Kolchin with Commentary, eds. Bass, H., et al., American Mathematical Society, Providence, 1999, pp. 505-526. Originally published in Ann. of Math. vol. 49, 1948, pp. 1-42. MR**9:561c****9.**, Galois theory of differential fields, in Selected Works of Ellis Kolchin with Commentary, eds. Bass, H., et al., American Mathematical Society, Providence, 1999, pp. 505-526. Originally published in Amer. J. Math. vol. 75, 1953, pp. 753-824. MR**15:394a****10.**E. R. Kolchin,*Constrained extensions of differential fields*, Advances in Math.**12**(1974), 141–170. MR**340227**, https://doi.org/10.1016/S0001-8708(74)80001-0**11.**Andy R. Magid,*Lectures on differential Galois theory*, University Lecture Series, vol. 7, American Mathematical Society, Providence, RI, 1994. MR**1301076****12.**J.-P. Ramis and J. Martinet,*Théorie de Galois différentielle et resommation*, Computer algebra and differential equations, Comput. Math. Appl., Academic Press, London, 1990, pp. 117–214 (French). MR**1038060****13.**C. Mitschi and M. F. Singer,*Connected linear groups as differential Galois groups*, J. Algebra**184**(1996), no. 1, 333–361. MR**1402584**, https://doi.org/10.1006/jabr.1996.0263**14.**Poizat, B., Les corps différentiellment clos, compagnons de route de la théorie des modéles, in Selected Works of Ellis Kolchin with Commentary, eds. Bass, H., et al., American Mathematical Society, Providence, 1999, pp. 555-566. CMP**99:09****15.**Singer, M., Direct and inverse problems in differential Galois theory, in Selected Works of Ellis Kolchin with Commentary, eds. Bass, H., et al., American Mathematical Society, Providence, 1999, pp. 527-554. CMP**99:09****16.**Carol Tretkoff and Marvin Tretkoff,*Solution of the inverse problem of differential Galois theory in the classical case*, Amer. J. Math.**101**(1979), no. 6, 1327–1332. MR**548884**, https://doi.org/10.2307/2374143**17.**Weil, A., Foundations of Algebraic Geometry, A.M.S. Colloquium Publ. 29, American Mathematical Society, New York (1946). MR**9:303c**

Review Information:

Reviewer: Andy R. Magid

Affiliation: University of Oklahoma

Email: amagid@ou.edu

Journal: Bull. Amer. Math. Soc.

**37**(2000), 337-342

MSC (2000): Primary 00B60, 12H05; Secondary 03C60, 11D99, 12F12, 12H20, 12Y05, 13A35, 13N10, 14E20, 14G20

DOI: https://doi.org/10.1090/S0273-0979-00-00862-4

Published electronically: February 1, 2000

Review copyright: © Copyright 2000 American Mathematical Society