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Book Information

Editor(s): H. Bass, A. Buium and P.J. Cassidy.
Title: Selected works of Ellis Kolchin
Additional book information: American Mathematical Society, Providence, RI, 1999, xiii + 639, $120.00, ISBN 0-8218-0542-8

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.: Deligne, P., Catégories tannakiennes, in The Grothendieck Festschrift Volume II, Cartier, P., et al., Birkhäuser, Boston, 1990, pp. 111-196. MR 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.: Kolchin, E., Differential Algebra and Algebraic Groups, Academic Press, New York (1973). MR 58:27929
7.: $\hbox to.55in{\hrulefill}$ , Differential Algebraic Groups, Academic Press, New York (1985). MR 87i:12016
8.: $\hbox to.55in{\hrulefill}$ , 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.: $\hbox to.55in{\hrulefill}$ , 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.: $\hbox to.55in{\hrulefill}$ , Constrained extensions 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 Adv. in Math. vol. 12, 1974, pp. 141-170. MR 49:4982
11.: Magid, A., Lectures on differential Galois theory, University Lecture Series, 7. Second printing with corrections, American Mathematical Society, Providence, RI, 1994. MR 95j:12008
12.: Martinet, J. and Ramis, J.-P., Théorie de Galois différentielle et resommation, in Computer Algebra and Differential Equations, ed. Tournier, E., Academic Press, New York, 1990, pp. 117-214. MR 91d:12014
13.: Mitschi, C. and Singer, M., Connected linear groups as differential Galois groups, J. Algebra, vol. 184, 1996, pp. 333-361. MR 97g:12004
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.: Tretkoff, C. and Tretkoff, M., Solution of the inverse problem of differential Galois theory in the classical case, Amer. J. Math. vol. 101, 1979, pp. 1327-1332. MR 80k:12033
17.: Weil, A., Foundations of Algebraic Geometry, A.M.S. Colloquium Publ. 29, American Mathematical Society, New York (1946). MR 9:303c

Reviewer(s):
Andy R. Magid
Affiliation: University of Oklahoma
Email: amagid@ou.edu

MSC (2000): Primary 00B60, 12H05; Secondary 03C60, 11D99, 12F12, 12H20, 12Y05, 13A35, 13N10, 14E20, 14G20
DOI: 10.1090/S0273-0979-00-00862-4
PII: S 0273-0979(00)00862-4
Posted: February 1, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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