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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Full text of review: PDF

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


References [Enhancements On Off] (What's this?)

  • 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 (92d:14002)
  • 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 (58 #27929)
  • 7. E. R. Kolchin, Differential algebraic groups, Pure and Applied Mathematics, vol. 114, Academic Press, Inc., Orlando, FL, 1985. MR 776230 (87i:12016)
  • 8. E. R. Kolchin, Algebraic matric groups and the Picard-Vessiot theory of homogeneous linear ordinary differential equations, Ann. of Math. (2) 49 (1948), 1–42. MR 0024884 (9,561c)
  • 9. E. R. Kolchin, Galois theory of differential fields, Amer. J. Math. 75 (1953), 753–824. MR 0058591 (15,394a)
  • 10. E. R. Kolchin, Constrained extensions of differential fields, Advances in Math. 12 (1974), 141–170. MR 0340227 (49 #4982)
  • 11. Andy R. Magid, Lectures on differential Galois theory, University Lecture Series, vol. 7, American Mathematical Society, Providence, RI, 1994. MR 1301076 (95j:12008)
  • 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 (91d:12014)
  • 13. C. Mitschi and M. F. Singer, Connected linear groups as differential Galois groups, J. Algebra 184 (1996), no. 1, 333–361. MR 1402584 (97g:12004), http://dx.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 (80k:12033), http://dx.doi.org/10.2307/2374143
  • 17. André Weil, Foundations of Algebraic Geometry, American Mathematical Society Colloquium Publications, vol. 29, American Mathematical Society, New York, 1946. MR 0023093 (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
DOI: http://dx.doi.org/10.1090/S0273-0979-00-00862-4
PII: S 0273-0979(00)00862-4
Published electronically: February 1, 2000
Review copyright: © Copyright 2000 American Mathematical Society