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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 31, Issue 4
  • October 1935, pp. 433-454

On the Structure of Abstract Algebras

  • Garrett Birkhoff (a1)
  • DOI:
  • Published online: 24 October 2008

The following paper is a study of abstract algebras qua abstract algebras. As no vocabulary suitable for this purpose is current, I have been forced to use a number of new terms, and extend the meaning of some accepted ones.

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L. Pontrjagin , “Theory of topological commutative groups”, Ann. of Math. 35 (1934), 361–88

E. H. Moore , “Tactical memoranda I–III”, Am. Jour. Math. 18 (1896), 264

G. Birkhoff , “Combinatorial relations in projective geometries”, Annals of Math. 36 (1935), 743–8.

M. H. Stone , “Boolean algebras and their application to topology”, Proc. U.S.A. Acad. 20 (1934), 197202.

A. C. Aitken , Edin. Math. Notes, 28 (1933), xviii–xxiii.

F. Klein , “Beiträge zur Theorie der Verbände”, Math. Zeitschrift, 39 (1934), 227239.

P. J. Daniell , “The modular difference of classes”, Bull. Amer. Math. Soc. 23 (1916), 446–50.

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