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Seligman received his bachelor's degree in 1950 from the [[University of Rochester]] and his PhD in 1954 from [[Yale University]] under [[Nathan Jacobson]] with thesis ''Lie algebras of prime characteristic''.<ref>{{MathGenealogyProject|id=4306}}</ref> After he received his PhD he was a Henry Burchard Fine Instructor at [[Princeton University]] from 1954–1956. In 1956 he became an instructor and from 1965 a full professor at Yale, where he was chair of the mathematics department from 1974 to 1977.
For the academic year 1958/59 he was a Fulbright Lecturer at the [[University of Münster]]. His doctoral students include [[James E. Humphreys]]
Since 1959 he has been married to Irene Schwieder and the couple has two daughters.
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