Nathan Jacobson

Nathan Jacobson (October 5, 1910 – December 5, 1999) was an American mathematician.[1]

Nathan Jacobson
Jacobson in 1974
Born	(1910-10-05)October 5, 1910 Warsaw, Congress Poland, Russian Empire
Died	December 5, 1999(1999-12-05) (aged 89) Hamden, Connecticut
Nationality	American
Alma mater	Princeton University (Ph.D. 1934) University of Alabama (B.S. 1930)
Known for	Mathematics textbooks; Jacobson–Bourbaki theorem; Jacobson's conjecture; Jacobson density theorem; Jacobson radical; Jacobson ring
Awards	AMS Steele Prize for Lifetime Achievement (1998)
Scientific career
Fields	Mathematics
Institutions	U.N.C. at Chapel Hill Johns Hopkins University Yale University
Doctoral advisor	Joseph Wedderburn
Doctoral students	Georgia Benkart Charles W. Curtis Craig Huneke Kevin McCrimmon George Seligman Daya-Nand Verma Maria Wonenburger

Biography

Born Nachman Arbiser[2] in Warsaw, Jacobson emigrated to America with his family in 1918. Recognized as one of the leading algebraists of his generation, he wrote more than a dozen standard textbooks. He graduated from the University of Alabama in 1930 and was awarded a doctorate in mathematics from Princeton University in 1934. While working on his thesis, Non-commutative polynomials and cyclic algebras, he was advised by Joseph Wedderburn.

Jacobson taught and researched at Bryn Mawr College (1935–1936), the University of Chicago (1936–1937), the University of North Carolina at Chapel Hill (1937–1943), and Johns Hopkins University (1943–1947) before joining Yale University in 1947. He remained at Yale until his retirement.

He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences. He served as president of the American Mathematical Society from 1971 to 1973, and was awarded their highest honour, the Leroy P. Steele prize for lifetime achievement, in 1998.[3] He was also vice-president of the International Mathematical Union from 1972 to 1974.

Selected works

Books

• Collected Mathematical Papers, 3 vols., 1989
• The theory of Rings. 1943[4]
• Lectures in Abstract Algebra.[5][6][7] 3 vols., Van Nostrand 1951, 1953, 1964, Reprint by Springer 1975 (Vol.1 Basic concepts, Vol.2 Linear Algebra, Vol.3 Theory of fields and Galois theory)
• Structure of Rings. AMS 1956[8]
• Lie Algebras. Interscience 1962[9]
• Structure and Representations of Jordan Algebras. AMS 1968[10]
• Exceptional Lie Algebras. Dekker 1971
• Basic Algebra. Freeman, San Francisco 1974, Vol. 1; 1980, Vol. 2; 2nd edition, Vol. 1. 1985. 2nd edition, Vol. 2. 1989.
• PI-Algebras. An Introduction. Springer 1975
• Finite-dimensional division algebras over fields 1996

Articles

• "Abstract derivation and Lie algebras". Trans. Amer. Math. Soc. 42: 206–224. 1937. doi:10.1090/s0002-9947-1937-1501922-7. MR 1501922.
• "p-algebras of exponent p". Bull. Amer. Math. Soc. 43: 667–670. 1937. doi:10.1090/s0002-9904-1937-06621-3. MR 1563614.
• "An application of E. H. Moore's determinant of a hermitian matrix". Bull. Amer. Math. Soc. 45: 745–748. 1939. doi:10.1090/s0002-9904-1939-07072-9. MR 0000219.
• "A note on hermitian forms". Bull. Amer. Math. Soc. 46: 264–268. 1940. doi:10.1090/s0002-9904-1940-07187-3. MR 0001957.
• "Restricted Lie algebras of characteristic p". Trans. Amer. Math. Soc. 50: 15–25. 1941. doi:10.1090/s0002-9947-1941-0005118-0. MR 0005118.
• "Schur's theorem on commutative algebras". Bull. Amer. Math. Soc. 50: 431–436. 1944. doi:10.1090/s0002-9904-1944-08169-x. MR 0010540.
• "The equation ${\displaystyle x'\equiv xd-dx=b}$". Bull. Amer. Math. Soc. 50: 902–905. 1944. doi:10.1090/s0002-9904-1944-08260-8. MR 0011290.
• "Structure theory of simple rings without finiteness assumptions". Trans. Amer. Math. Soc. 57: 228–245. 1945. doi:10.1090/s0002-9947-1945-0011680-8. MR 0011680.
• "The radical and semi-simplicity for arbitrary rings". Amer. J. Math. 67: 300–322. 1945. doi:10.2307/2371731. MR 0012271.
• "Structure theory for algebras of bounded degree". Ann. Math. 46: 695–707. 1945. doi:10.2307/1969205. MR 0014083.
• "A topology for the set of primitive ideals in an arbitrary ring". Proc Natl Acad Sci U S A. 31: 333–338. 1945. doi:10.1073/pnas.31.10.333. PMC 1078836. PMID 16588704.
• "The center of a Jordan ring". Bull. Amer. Math. Soc. 54: 316–322. 1948. doi:10.1090/s0002-9904-1948-08993-5. MR 0024422.
• with F. D. Jacobson: "Classification and representation of semi-simple Jordan algebras". Trans. Amer. Math. Soc. 65: 141–169. 1949. doi:10.1090/s0002-9947-1949-0029367-8. MR 0029367.
• "Lie and Jordan triple systems". Amer. J. Math. 71: 149–170. 1949. doi:10.2307/2372102. MR 0028305.
• with C. E. Rickart: "Jordan homomorphisms of rings". Trans. Amer. Math. Soc. 69: 479–502. 1950. doi:10.1090/s0002-9947-1950-0038335-x. MR 0038335.
• "Some remarks on one-sided inverses". Proc. Amer. Math. Soc. 1: 352–355. 1950. doi:10.1090/s0002-9939-1950-0036223-1. MR 0036223.
• "General representation theory of Jordan algebras". Trans. Amer. Math. Soc. 70: 509–530. 1951. doi:10.1090/s0002-9947-1951-0041118-9. MR 0041118.
• "Completely reducible Lie algebras of linear transformations". Proc. Amer. Math. Soc. 2: 105–113. 1951. doi:10.1090/s0002-9939-1951-0049882-5. MR 0049882.
• with C. E. Rickart: "Homomorphisms of Jordan rings of self-adjoint elements". Trans. Amer. Math. Soc. 72: 310–322. 1952. doi:10.1090/s0002-9947-1952-0046346-5. MR 0046346.
• "Operator commutativity in Jordan algebras". Proc. Amer. Math. Soc. 3: 973–976. 1952. doi:10.1090/s0002-9939-1952-0051828-1. MR 0051828.
• "A note on automorphisms and derivations of Lie algebras". Proc. Amer. Math. Soc. 6: 281–283. 1955. doi:10.1090/s0002-9939-1955-0068532-9. MR 0068532.
• "Commutative restricted Lie algebras". Proc. Amer. Math. Soc. 6: 476–481. 1955. doi:10.1090/s0002-9939-1955-0071721-0. MR 0071721.

See also

• Jacobson–Bourbaki theorem
• Jacobson's conjecture
• Jacobson density theorem
• Jacobson radical
• Jacobson ring

References

1. "Nathan Jacobson (1910-1999)" (PDF). Notices of the AMS. 47: 1061–71. 1999.
2. "Nathan Jacobson". American National Biography Online. Retrieved 12 January 2014.
3. "1998 Steele Prizes" (PDF). Notices of the AMS. 48: 504–8. 1998.
4. Baer, Reinhold (1946). "Review: Nathan Jacobson, The theory of rings". Bull. Amer. Math. Soc. 52 (3): 220–222. doi:10.1090/s0002-9904-1946-08527-4.
5. Mills, W. H. (1952). "Review: N. Jacobson, Lectures in abstract algebra. Vol. I. Basic concepts". Bull. Amer. Math. Soc. 58 (5): 579–580. doi:10.1090/s0002-9904-1952-09628-2.
6. Dieudonné, J. (1953). "Review: N. Jacobson, Lectures in abstract algebra. Vol. II. Linear algebra". Bull. Amer. Math. Soc. 59 (5): 480–483. doi:10.1090/s0002-9904-1953-09727-0.
7. Herstein, I. N. (1967). "Book Review: Nathan Jacobson, Lectures in abstract algebra, Vol. III, Theory of fields and Galois theory". Bull. Amer. Math. Soc. 73 (1): 44–46. doi:10.1090/s0002-9904-1967-11628-8.
8. Rosenberg, Alex (1957). "Review: Nathan Jacobson, Structure of rings" (PDF). Bull. Amer. Math. Soc. 63 (1): 46–50. doi:10.1090/s0002-9904-1957-10071-8.
9. Hochschild, G. (1963). "Review: Nathan Jacobson, Lie algebras". Bull. Amer. Math. Soc. 69 (1): 37–39. doi:10.1090/s0002-9904-1963-10841-1.
10. Schafer, R. D. (1973). "Review: Structure and Representations of Jordan Algebras by Nathan Jacobson". Bull. Amer. Math. Soc. 79 (3): 509–514. doi:10.1090/S0002-9904-1973-13175-1.

External links

• Nathan Jacobson at the Mathematics Genealogy Project
• O'Connor, John J.; Robertson, Edmund F., "Nathan Jacobson", MacTutor History of Mathematics archive, University of St Andrews.
• An interview with William L. Duren, Nathan Jacobson, and Edward J. McShane about their experiences at Princeton