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词条 Nathan Jacobson
释义

  1. Biography

  2. Selected works

     Books  Articles 

  3. See also

  4. References

  5. External links

{{Infobox scientist
| name = Nathan Jacobson
| image = Nathan Jacobson.jpg
| image_size =
| alt =
| caption = Jacobson in 1974
| birth_date = {{birth date|1910|10|05}}
| birth_place = Warsaw, Congress Poland, Russian Empire
| death_date = {{Death date and age|1999|12|05|1910|10|05}}
| death_place = Hamden, Connecticut
| residence =
| citizenship =
| nationality = American
| fields = Mathematics
| workplaces = U.N.C. at Chapel Hill
Johns Hopkins University
Yale University
| alma_mater = Princeton University (Ph.D. 1934)
University of Alabama (B.S. 1930)
| doctoral_advisor = Joseph Wedderburn
| academic_advisors =
| doctoral_students = Georgia Benkart
Charles W. Curtis
Craig Huneke
Kevin McCrimmon
George Seligman
Daya-Nand Verma
Maria Wonenburger
| notable_students =
| known_for = Mathematics textbooks; Jacobson–Bourbaki theorem; Jacobson's conjecture; Jacobson density theorem; Jacobson radical; Jacobson ring
| author_abbrev_bot =
| author_abbrev_zoo =
| influences =
| influenced =
| awards = AMS Steele Prize for Lifetime Achievement (1998)
| signature =
| signature_alt =
| footnotes =
| spouse =
}}Nathan Jacobson (October 5, 1910 – December 5, 1999) was an American mathematician.[1]

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
  • [https://books.google.com/books/about/The_Theory_of_Rings.html?id=pmhOBkn77lAC 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]
  • [https://books.google.com/books/about/Structure_and_Representations_of_Jordan.html?id=aAGWAwAAQBAJ Structure and Representations of Jordan Algebras.] AMS 1968[10]
  • [https://books.google.com/books/about/Exceptional_Lie_Algebras.html?id=Ay48FcOHHlAC Exceptional Lie Algebras.] Dekker 1971
  • Basic Algebra. Freeman, San Francisco 1974, Vol. 1; 1980, Vol. 2; {{cite book|title=2nd edition, Vol. 1|year=1985|url=https://books.google.com/books/about/Basic_Algebra_I.html?id=JHFpv0tKiBAC}} {{cite book|title=2nd edition, Vol. 2|year=1989|url=https://books.google.com/books/about/Basic_Algebra_II.html?id=hn75exNZZ-EC}}
  • PI-Algebras. An Introduction. Springer 1975
  • [https://books.google.com/books/about/Finite_Dimensional_Division_Algebras_Ove.html?id=gdl-l2ZmcOkC Finite-dimensional division algebras over fields] 1996

Articles

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

See also

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

References

1. ^{{Cite journal|title=Nathan Jacobson (1910-1999)|journal=Notices of the AMS|year=1999|volume=47|pages=1061–71|url=http://www.ams.org/notices/200009/mem-jacobson.pdf}}
2. ^{{cite web | url=http://www.anb.org/articles/13/13-02672.html | title=Nathan Jacobson | publisher=American National Biography Online | accessdate=12 January 2014}}
3. ^{{Cite journal|title=1998 Steele Prizes|journal=Notices of the AMS|year=1998|volume=48|pages=504–8|url=http://www.ams.org/notices/199804/comm-steele-prizes.pdf}}
4. ^{{cite journal|author=Baer, Reinhold|title=Review: Nathan Jacobson, The theory of rings|journal=Bull. Amer. Math. Soc.|year=1946|volume=52|issue=3|pages=220–222|url=http://projecteuclid.org/euclid.bams/1183507765|doi=10.1090/s0002-9904-1946-08527-4}}
5. ^{{cite journal|author=Mills, W. H.|title=Review: N. Jacobson, Lectures in abstract algebra. Vol. I. Basic concepts|journal=Bull. Amer. Math. Soc.|year=1952|volume=58|issue=5|pages=579–580|url=http://projecteuclid.org/euclid.bams/1183517376|doi=10.1090/s0002-9904-1952-09628-2}}
6. ^{{cite journal|author=Dieudonné, J.|title=Review: N. Jacobson, Lectures in abstract algebra. Vol. II. Linear algebra|journal=Bull. Amer. Math. Soc.|year=1953|volume=59|issue=5|pages=480–483|url=http://projecteuclid.org/euclid.bams/1183518209|doi=10.1090/s0002-9904-1953-09727-0}}
7. ^{{cite journal|author=Herstein, I. N.|title=Book Review: Nathan Jacobson, Lectures in abstract algebra, Vol. III, Theory of fields and Galois theory|journal=Bull. Amer. Math. Soc.|year=1967|volume=73|issue=1|pages=44–46|url=http://projecteuclid.org/euclid.bams/1183528607|doi=10.1090/s0002-9904-1967-11628-8}}
8. ^{{cite journal|last=Rosenberg|first= Alex|authorlink=Alex F. T. W. Rosenberg|title=Review: Nathan Jacobson, Structure of rings|journal=Bull. Amer. Math. Soc.|year=1957|volume=63|issue=1|pages=46–50|url=http://www.ams.org/journals/bull/1957-63-01/S0002-9904-1957-10071-8/S0002-9904-1957-10071-8.pdf|doi=10.1090/s0002-9904-1957-10071-8}}
9. ^{{cite journal|author=Hochschild, G.|title=Review: Nathan Jacobson, Lie algebras|journal=Bull. Amer. Math. Soc.|year=1963|volume=69|issue=1|pages=37–39|url=http://projecteuclid.org/euclid.bams/1183525000|doi=10.1090/s0002-9904-1963-10841-1}}
10. ^{{cite journal|title=Review: Structure and Representations of Jordan Algebras by Nathan Jacobson|author=Schafer, R. D.|authorlink=Richard D. Schafer|journal=Bull. Amer. Math. Soc.|volume=79|issue=3|year=1973|pages=509–514|doi=10.1090/S0002-9904-1973-13175-1}}

External links

  • {{MathGenealogy|id=4291}}
  • {{MacTutor Biography|id=Jacobson}}
  • [https://web.archive.org/web/20150310080254/http://www.princeton.edu/~mudd/finding_aids/mathoral/pmc08.htm An interview with William L. Duren, Nathan Jacobson, and Edward J. McShane about their experiences at Princeton]
{{AMS Presidents}}{{Authority control}}{{DEFAULTSORT:Jacobson, Nathan}}

15 : 1910 births|Members of the United States National Academy of Sciences|1999 deaths|American people of Polish-Jewish descent|20th-century American mathematicians|Algebraists|University of Alabama alumni|Princeton University alumni|Bryn Mawr College faculty|University of North Carolina at Chapel Hill faculty|Johns Hopkins University faculty|Yale University faculty|People from Warsaw|Presidents of the American Mathematical Society|Guggenheim Fellows

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