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**
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.
E. R. Kolchin, *Differential algebra and algebraic groups*, Pure and Applied Mathematics, Vol. 54, Academic Press, New York-London, 1973. MR **0568864**
E. R. Kolchin, *Differential algebraic groups*, Pure and Applied Mathematics, vol. 114, Academic Press, Inc., Orlando, FL, 1985. MR **776230**
Garrett Birkhoff and Morgan Ward, *A characterization of Boolean algebras*, Ann. of Math. (2) **40** (1939), 609–610. MR **9**, DOI 10.2307/1968945
Sam Perlis, *Maximal orders in rational cyclic algebras of composite degree*, Trans. Amer. Math. Soc. **46** (1939), 82–96. MR **15**, DOI 10.1090/S0002-9947-1939-0000015-X
E. R. Kolchin, *Constrained extensions of differential fields*, Advances in Math. **12** (1974), 141–170. MR **340227**, DOI 10.1016/S0001-8708(74)80001-0
Andy R. Magid, *Lectures on differential Galois theory*, University Lecture Series, vol. 7, American Mathematical Society, Providence, RI, 1994. MR **1301076**, DOI 10.1090/ulect/007
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**
C. Mitschi and M. F. Singer, *Connected linear groups as differential Galois groups*, J. Algebra **184** (1996), no. 1, 333–361. MR **1402584**, DOI 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**
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**, DOI 10.2307/2374143
Garrett Birkhoff and Morgan Ward, *A characterization of Boolean algebras*, Ann. of Math. (2) **40** (1939), 609–610. MR **9**, DOI 10.2307/1968945
**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
**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.**- Kolchin, E., Differential Algebra and Algebraic Groups, Academic Press, New York (1973). MR
**0568864**
**7.**- , Differential Algebraic Groups, Academic Press, New York (1985). MR
**0776230**
**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.**- , 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
**0340227**
**11.**- Magid, A., Lectures on differential Galois theory, University Lecture Series, 7. Second printing with corrections, American Mathematical Society, Providence, RI, 1994. MR
**1301076**
**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
**1038060**
**13.**- Mitschi, C. and Singer, M., Connected linear groups as differential Galois groups, J. Algebra, vol. 184, 1996, pp. 333-361. MR
**1402584**
**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
**0548884**
**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

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

Published electronically:
February 1, 2000

Review copyright:
© Copyright 2000
American Mathematical Society