David Kent Harrison Explained

Birth Date:	6 April1931
Birth Place:	Massachusetts
Death Date:	21 December1999
Death Place:	Barnstable, Massachusetts
Alma Mater:	Princeton University
Occupation:	mathematician
Awards:	Guggenheim Fellowship

David Kent Harrison (6 April 1931, Massachusetts – 21 December 1999, Barnstable, Massachusetts) was an American mathematician, specializing in algebra, particularly homological algebra and valuation theory.

He completed his Ph.D. at Princeton University in 1957; his dissertation, titled On torsion free abelian groups, was written under the supervision of Emil Artin.

Harrison was a faculty member from 1959 to 1963 at the University of Pennsylvania^[1] and from 1963 to 1993 at the University of Oregon, retiring there as professor emeritus in 1993.^[2]

He developed a commutative cohomology theory for commutative algebras.^[3] Along with his colleague Marie A. Vitulli, he developed a unified valuation theory for rings with zero divisors that generalized both Krull and Archimedean valuations.^[4]

He was a Guggenheim Fellow for the academic year 1963–1964.^[5] He supervised 28 doctoral students including Joel Cunningham. Ann Hill Harrison endowed the Harrison Memory Award for outstanding mathematical students at the University of Oregon.^[2] He is survived by his son, composer and pianist Michael Harrison, a Guggenheim Fellow for the academic year 2018–2019,^[6] and his daughter Jo Ellen Harrison.

Selected publications

• 1959. Infinite abelian groups and homological methods. Annals of Mathematics. 69. 2. 366–391. 10.2307/1970188. 1970188. Harrison. D. K.. 10338.dmlcz/101186. free.
• 1963. 10.1090/S0002-9947-1963-0142545-X. Abelian extensions of arbitrary fields. Transactions of the American Mathematical Society. 106. 2. 230–235. Harrison. D. K.. free.
• with J. M. Irwin, C. L. Peercy, and E. A. Walker: 1963. High extensions of Abelian groups. Acta Mathematica Hungarica. 14. 3–4. 319–330. 10.1007/BF01895718. free. Harrison. D. K.. Irwin. J. M.. Peercy. C. L.. Walker. E. A.. 117185748.
• Book: On the structure of Ext. In: Abelian Groups (Proc. Sympos., New Mexico State Univ., 1962). 1963. 195–209.
• Book: 1965. Abelian extensions of commutative rings. American Mathematical Society.
• with Stephen U. Chase and Alex F. T. W. Rosenberg: Book: 1965. Galois theory and cohomology of commutative rings. American Mathematical Society.
• Book: 1966. Finite and infinite primes for rings and fields. Memoirs of the American Mathematical Society, No. 68.

  62 pp.

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• with Joel Cunningham: Book: 1970. Witt rings. Department of Mathematics, University of Kentucky.
• with Hoyt D. Warner: 1973. Infinite primes of fields and completions. Pacific Journal of Mathematics. 45. 1. 201–216. 10.2140/pjm.1973.45.201. Harrison. David. Warner. Hoyt. free.
• 1975. A Grothendieck ring of higher degree forms. Journal of Algebra. 35. 1–3. 123–138. 10.1016/0021-8693(75)90039-3. Harrison. D.K. free.
• Double coset and orbit spaces. 1979. Pacific Journal of Mathematics. 80. 2. 451–491. 10.2140/pjm.1979.80.451. Harrison. David. free.
• 1985. 10.1090/S0002-9939-1985-0801318-2. Bipowers in number fields. Proceedings of the American Mathematical Society. 95. 2. 174–178. Harrison. D. K.. free.
  • 1986. 10.1090/S0002-9939-1986-0835904-1. Erratum to: Bipowers in number fields. Proceedings of the American Mathematical Society. 97. 2. 378. Harrison. D. K.. free.
• with Cornelius Greither: 1986. A Galois correspondence for radical extensions of fields. Journal of Pure and Applied Algebra. 46. 257–270.
• with Bodo Pareigis: 1985. Witt rings of higher degree forms. Communications in Algebra. 16. 6. 1275–1313.
• with M. A. Vitulli: 1989. Complex-valued places and CMC subsets of a field. Communications in Algebra. 17. 10. 2529–2537. 10.1080/00927878908823860. Harrison. D.K.. Vltulli. M A..
• with Frank DeMeyer and Rick Miranda: Book: 1989. Quadratic forms over Q and Galois extensions of commutative rings. Memoirs of the American Mathematical Society, Volume 77, Number 394. Providence, Rhode Island. 9780821824573. Demeyer. Frank. Harrison. David. Miranda. Rick.
• with C. Greither: 1989. On the monoid of tame extensions. Transactions of the American Mathematical Society. 311. 2. 657–682. 10.1090/S0002-9947-1989-0978371-7. Greither. Cornelius. Harrison. D. K.. free.

External links

• Web site: Princeton University (1953-1956). Mathematics & Physics. "Biographical Sketch of Hugh Everett, III" by Eugene Shikhovtsev, space.mit.edu. (1955 photograph of, left to right, Charles W. Misner, Hale Trotter, Niels Bohr, Hugh Everett III, and David Harrison)
• David K. Harrisons's Author Profile Page on MathSciNet

Notes and References

1. Web site: Faculty History. Department of Mathematics, University of Pennsylvania.
2. Web site: Former Faculty. Department of Mathematics, University of Oregon.
3. Harrison . D. K. . Commutative Algebras and Cohomology . Transactions of the American Mathematical Society . 1962 . 104. 2 . 191–204 . 0142607 . 10.1090/S0002-9947-1962-0142607-6 . 3 April 2020. free .
4. Harrison . D. K. . Vitulli . Marie A. . V-Valuations of a Commutative Ring I . J. Algebra . 1989 . 65 . 3 . 264–292 . 1024992. 10.1016/0021-8693(89)90305-0 . free .
5. Web site: David Kent Harrison. John Simon Guggenheim Memorial Foundation.
6. Web site: Michael Harrison. John Simon Guggenheim Memorial Foundation.