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Horace Yomishi Mochizuki

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Horace Yomishi Mochizuki (18 May 1937 – 9 June 1989) was an American mathematician known for his contributions to group theory. Mochizuki received a special award from the National Science Foundation for his work on the Burnside problem.

Biography

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Mochizuki was born in California on 18 May 1937 from parents of Japanese ancestry.[1] Following the Imperial Japan's attack on Pearl Harbor, President Roosevelt authorized on 19 February 1942 the deportation and internment of Japanese Americans with Executive Order 9066 which allowed regional military commanders to designate "military areas" from which "any or all persons may be excluded". This authority was used to declare that all people of Japanese ancestry were excluded from the West Coast, including all of California and parts of Oregon, Washington, and Arizona, except for those in government camps. Mochizuki was interned with his family in the Jerome War Relocation Center in Arkansas.[2] After World War II, the family moved back to Madera, California, where Horace won the Madera County spelling bee in 1951.[3]

Mochizuki received his doctoral degree from the University of Washington with a dissertation work entitled "Finitistic homological dimensions and duality theory for rings".[4] He began teaching at University of California, Santa Barbara in 1965.[5]

Mochizuki died on 9 June 1989 from cancer of the pancreas. His wife, Keiko, committed suicide two days later by drowning in the Pacific Ocean.[5]

Work

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At the beginning of his academic career, Mochizuki's worked on ring theory.[6][7][8] He started to cooperate with Seymour Bachmuth on group theory.[9][10][11] For his work on Burnside groups, Mochizuki received a special award from the National Science Foundation for "projects of high scientific merit involving scientists with a record of outstanding research accomplishments..."[1][11]

Mochizuki is known for a non-commutative version of "Kolchin's Theorem" that solved a theorem of Ivan Kaplansky and for his work on automorphism groups with Bachmuth.[12][13][14][15]

References

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  1. ^ a b Bachmuth, Seymour; Millett, Kenneth; Robertson, James (1991). "Horace Y Mochizuki: In Memoriam". Groups St Andrews 1989. Cambridge University Press. pp. 38–45. doi:10.1017/cbo9780511721236.006. ISBN 978-0-511-72123-6.
  2. ^ Parker, Tom (10 March 1943). "Two young pre-school students play in the sand box at the Jerome Center grade school. Left, Sei Asaki; right, Horace Mochizuki. (Japanese Americans – Evacuation and relocation, 1942–1945 – Photographs)". Online Archive of California. Retrieved 2018-09-29.
  3. ^ "Horace Mochizuki, 13, Wins Spelling Contest". Madera Daily News-Tribume. 1951-04-10. p. 1. Retrieved 2020-09-04. Thirteen-year-old Horace Mochizuki of Ripperdan school correctly spelled "chaperon" today and captured first place as Madera county's champion speller.
  4. ^ "Horace Mochizuki – The Mathematics Genealogy Project". www.genealogy.math.ndsu.nodak.edu. Retrieved 2018-09-29.
  5. ^ a b Fitzsimons, Matt (1989-06-26). "Math Professor Dies, Wife's Death Follows". Daily Nexus. Santa Barbara, CA: University of California, Santa Barbara. p. 1. Retrieved 2020-09-04.
  6. ^ Mochizuki, Horace (1965). "Finitistic global dimension for rings". Pacific Journal of Mathematics. 15 (1): 249–258. doi:10.2140/pjm.1965.15.249. ISSN 0030-8730.
  7. ^ Mochizuki, H. Y. (1965). "On the Double Commutator Algebra of QF-3 Algebras". Nagoya Mathematical Journal. 25: 221–230. doi:10.1017/S0027763000011557. ISSN 0027-7630.
  8. ^ Wu, L. E. T.; Mochizuki, H. Y.; Jans, J. P. (1966). "A characterization of QF-3 rings". Nagoya Mathematical Journal. 27 (Part): 7–13. doi:10.1017/S0027763000011806. ISSN 0027-7630.
  9. ^ Bachmuth, S.; Mochizuki, H. Y. (1966). "Cyclotomic ideals in group rings". Bulletin of the American Mathematical Society. 72 (6): 1018–1021. doi:10.1090/S0002-9904-1966-11623-3. ISSN 0002-9904.
  10. ^ Bachmuth, S.; Mochizuki, H. Y. (1967). "Automorphisms of a class of metabelian groups. II". Transactions of the American Mathematical Society. 127 (2): 294. doi:10.1090/S0002-9947-1967-0213437-6. ISSN 0002-9947.
  11. ^ a b Mochizuki, Horace Y. (1974), "On groups of exponent four: A criterion for nonsolvability", Proceedings of the Second International Conference on the Theory of Groups, Lecture Notes in Mathematics, vol. 372, Springer Berlin Heidelberg, pp. 499–503, doi:10.1007/bfb0065206, ISBN 978-3-540-06845-7
  12. ^ Mochizuki, H. Y. (1978). "Unipotent matrix groups over division rings" (PDF). Canadian Mathematical Bulletin. 21 (2): 249–250. doi:10.4153/cmb-1978-043-2. ISSN 1496-4287.
  13. ^ Kaplansky, Irving (1977), "The Engel–Kolchin theorem revisited", Contributions to Algebra, Elsevier, pp. 233–237, doi:10.1016/b978-0-12-080550-1.50022-6, ISBN 978-0-12-080550-1
  14. ^ Bachmuth, S.; Mochizuki, H. Y. (1975). "Automorphisms of solvable groups". Bulletin of the American Mathematical Society. 81 (2): 420–422. doi:10.1090/S0002-9904-1975-13767-0. ISSN 0002-9904.
  15. ^ Bachmuth, Seymour; Mochizuki, Horace Y. (1978-11-01). "IA-automorphisms of the free metabelian group of rank 3". Journal of Algebra. 55 (1): 106–115. doi:10.1016/0021-8693(78)90194-1. ISSN 0021-8693.
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