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Sweedler received his Ph.D from the Massachusetts Institute of Technology in 1965 with thesis Cocommutative Hopf Algebras with Antipode and with advisor Bertram Kostant. Sweedler wrote Hopf Algebras (1969), which became the standard reference book on Hopf algebras. He, with Harry P. Allen, used Hopf algebras to prove in 1969 a famous 25-year-old conjecture of Jacobson about the forms of generalized Witt algebras over algebraically closed fields of finite characteristic. From 1965 to the mid 1980s Sweeder worked on commutative algebra and related disciplines. Since the mid 1980s Sweedler has worked primarily on computer algebra. His research resulted in his position as director of the Army Center of Excellence for computer algebra.
with Darrell E. Halle and R. Larson: "A new invariant for C over R: almost invertible cohomology theory and the classification of idempotent cohomology classes and algebras by partially ordered sets with a Galois group action". Amer. J. Math. 105: 689-814. 1983. doi:10.2307/2374320.
with I. Rubio and C. Heegard: Gröbner bases for linear recursion relations on m-D arrays and applications to decoding, Proc. IEEE Int'l Symp. on Information Theory, June 29-July 4, 1997, Ulm, Germany.
with K. Shirayanagi: Remarks on automatic algorithm stabilization, invited contribution to (fourth) IMACS Conf. on Appl. of Computer Algebra (1998).