David Kent Harrison

Born| 6 April1931

Massachusetts

Died| 21 December1999

Barnstable, Massachusetts

Alma mater| Princeton University
Occupation| mathematician
Awards| Guggenheim Fellowship

Short description: American mathematician

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.[1]

Harrison was a faculty member from 1959 to 1963 at the University of Pennsylvania[2] and from 1963 to 1993 at the University of Oregon, retiring there as professor emeritus in 1993.[3]

He developed a commutative cohomology theory for commutative algebras.[4] 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.[5]

He was a Guggenheim Fellow for the academic year 1963–1964.[6] He supervised 28 doctoral students including Joel Cunningham.[1] Ann Hill Harrison endowed the Harrison Memory Award for outstanding mathematical students at the University of Oregon.[3] He is survived by his son, composer and pianist Michael Harrison, a Guggenheim Fellow for the academic year 2018–2019,[7] and his daughter Jo Ellen Harrison.

## Selected publications

* Harrison, D. K. (1959). "Infinite abelian groups and homological methods". Annals of Mathematics 69 (2): 366–391. doi:10.2307/1970188.
* Harrison, D. K. (1963). "Abelian extensions of arbitrary fields". Transactions of the American Mathematical Society 106 (2): 230–235. doi:10.1090/S0002-9947-1963-0142545-X.
* with J. M. Irwin, C. L. Peercy, and E. A. Walker: Harrison, D. K.; Irwin, J. M.; Peercy, C. L.; Walker, E. A. (1963). "High extensions of Abelian groups". Acta Mathematica Hungarica 14 (3–4): 319–330. doi:10.1007/BF01895718.
* "On the structure of Ext". In: Abelian Groups (Proc. Sympos., New Mexico State Univ., 1962). 1963. pp. 195–209.
* Abelian extensions of commutative rings. American Mathematical Society. 1965.
* with Stephen U. Chase and Alex F. T. W. Rosenberg:  Galois theory and cohomology of commutative rings. American Mathematical Society. 1965.
* Finite and infinite primes for rings and fields. Memoirs of the American Mathematical Society, No. 68. 1966; 62 pp.
* with Joel Cunningham:  Witt rings. Department of Mathematics, University of Kentucky. 1970.
* with Hoyt D. Warner: Harrison, David; Warner, Hoyt (1973). "Infinite primes of fields and completions". Pacific Journal of Mathematics 45 (1): 201–216. doi:10.2140/pjm.1973.45.201.
* Harrison, D.K (1975). "A Grothendieck ring of higher degree forms". Journal of Algebra 35 (1–3): 123–138. doi:10.1016/0021-8693(75)90039-3. http://core.ac.uk/download/pdf/82089961.pdf.
* Harrison, David (1979). "Double coset and orbit spaces". Pacific Journal of Mathematics 80 (2): 451–491. doi:10.2140/pjm.1979.80.451.
* Harrison, D. K. (1985). "Bipowers in number fields". Proceedings of the American Mathematical Society 95 (2): 174–178. doi:10.1090/S0002-9939-1985-0801318-2.
* Harrison, D. K. (1986). "Erratum to: Bipowers in number fields". Proceedings of the American Mathematical Society 97 (2): 378. doi:10.1090/S0002-9939-1986-0835904-1.
* with Cornelius Greither: "A Galois correspondence for radical extensions of fields". Journal of Pure and Applied Algebra 46: 257–270. 1986. http://core.ac.uk/download/pdf/82551655.pdf.
* with Bodo Pareigis: "Witt rings of higher degree forms". Communications in Algebra 16 (6): 1275–1313. 1985.
* with M. A. Vitulli: Harrison, D.K.; Vltulli, M A. (1989). "Complex-valued places and CMC subsets of a field". Communications in Algebra 17 (10): 2529–2537. doi:10.1080/00927878908823860.
* with Frank DeMeyer and Rick Miranda: Demeyer, Frank; Harrison, David; Miranda, Rick (1989). Quadratic forms over Q and Galois extensions of commutative rings. Memoirs of the American Mathematical Society, Volume 77, Number 394. Providence, Rhode Island. ISBN 9780821824573. https://books.google.com/books?id=GV7UCQAAQBAJ.
* with C. Greither: Greither, Cornelius; Harrison, D. K. (1989). "On the monoid of tame extensions". Transactions of the American Mathematical Society 311 (2): 657–682. doi:10.1090/S0002-9947-1989-0978371-7.

## References

1. ↑ 1.0 1.1 David Kent Harrison at the Mathematics Genealogy Project
2. ↑ "Faculty History". http://www.math.upenn.edu/about/department-history/faculty-history.
3. ↑ 3.0 3.1 "Former Faculty". http://math.uoregon.edu/people/former-faculty.
4. ↑ Harrison, D. K. (1962). "Commutative Algebras and Cohomology". Transactions of the American Mathematical Society 104 (2): 191–204. doi:10.1090/S0002-9947-1962-0142607-6. https://www.ams.org/journals/tran/1962-104-02/S0002-9947-1962-0142607-6/home.html. Retrieved 3 April 2020.
5. ↑ Harrison, D. K.; Vitulli, Marie A. (1989). "V-Valuations of a Commutative Ring I". J. Algebra 65 (3): 264–292. doi:10.1016/0021-8693(89)90305-0.
6. ↑ "David Kent Harrison". https://www.gf.org/fellows/all-fellows/david-kent-harrison/.
7. ↑ "Michael Harrison". https://www.gf.org/fellows/all-fellows/michael-harrison/.

## External links

* "Princeton University (1953-1956). Mathematics & Physics". http://space.mit.edu/home/tegmark/everett/everett04_princeton.html. (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

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