algebras. He then showed that every finite-dimensional semisimple algebra can be constructed as a direct sum of simple algebras and that every simple algebra is isomorphic to a matrix algebra for some division ring. The Artin–Wedderburn theorem generalises these results to algebras with the descending chain condition. His best known book is his Lectures on Matrices (1934), which Jacobson praised as follows: About Wedderburn's teaching: See also Hypercomplex numbers Wedderburn–Etherington number Wedderburn's little theorem Wedderburn's theorem (division ring) Wedderburn's theorem (simple ring) Artin–Wedderburn theorem References Further reading Robert Hooke (1984) Recollections of Princeton, 1939–1941 Karen Parshall (1983) "In pursuit of the finite division algebra theorem and beyond: Joseph H M Wedderburn, Leonard Dickson, and Oswald Veblen," Archives of International History of Science 33: 274–99. Karen Parshall (1985) "Joseph H. M. Wedderburn and the structure theory of algebras," Archive for History of Exact Sciences 32: 223–349. Karen Parshall (1992) "New Light on the Life and Work of Joseph Henry Maclagan Wedderburn (1882–1948)," in Menso Folkerts et al. (eds.): Amphora: Festschrift für Hans Wußing zu seinem 65. Geburtstag, Birkhäuser Verlag, 523–537. 1882 births 1948 deaths 20th-century American mathematicians People from Forfar People educated at Forfar Academy People educated at George Watson's College Alumni of the University of Edinburgh Leipzig University alumni Humboldt University of Berlin alumni University of Chicago alumni Academics of the University of Edinburgh Princeton University faculty Fellows of the Royal Society of Edinburgh Fellows of the Royal Society Seaforth Highlanders officers Royal Engineers officers Algebraists British Army personnel of World War I Scottish emigrants to the United States Scottish mathematicians Military personnel from Angus, Scotland