격자론의 기원

  • 홍영희 (숙명여자대학교 수학과)
  • 발행 : 1999.12.01

초록

This paper deals with the origin of the concept of lattices in mathematics and its development until 1930's. Although it is purely mathematical, its formation is due to the development of symbolic logic Further, logicians were mostly concerned about how to imitate the methods and duplicate the problems of algebra but not the application to mathematics. The first purely mathematical approach was given by Dedekind and his results were neglected and then reappeared in 1930's.

키워드

참고문헌

  1. Distributive Lattices R. Balbes;P. Dwinger
  2. Proc. Camb. Phil. Soc. v.29 On the combination of subalgebras G. Birkhoff
  3. Proc. Camb. Phil. Soc. v.30 Note on the paper 'On the combination of subalgebras G. Birkhoff
  4. Proc. Camb. Phil. Soc. v.30 Applications of lattice algebra G. Birkhoff
  5. Annals of Math v.36 Combinatorial relations in projective geometries G. Birkhoff
  6. Lattice Theory, Amer. Math. Soc. Coll. Pub. XXV, Amer. Math. Soc. Providence (1st ed.) 1940(2nd ed.) 1948, (3rd ed.) G. Birkhoff
  7. Annals of Math v.37 The logic of quantum mechanics G. Birkhoff;J. von Neumann
  8. Paradoxien des Unendlichen B. Bolzano;F. Prihonsky(ed.);C. H. Reclam
  9. The Mathematical Analysis of Logic G. Boole
  10. An Investigation of the Laws of Thought G. Boole
  11. Stetigkeit und Irrational Zahlen R. Dedekind
  12. Festschrift Techn. Hoch Braunschweig(1897) and Ges. Werke v.II Uber Zerlegungen von Zahlen durch ihre grossten gemeinsamen Teiler R. Dedekind
  13. Math. Ann, and Ges. Werke v.53;II Uber die von drei Moduln erzeugte Dualgruppe R. Dedekind
  14. Gesammelte mathermatische Werke v.3 R. Dedekind
  15. Werke v.X C. F. Gauss
  16. Gesammelte mathematische Werke v.6 H. Grassmann
  17. Sitzungsber. Preuss Akad. Wiss. Phys.-math. Klasse Die formalen Reglen der intuitionistischen Logik A. Heyting
  18. Pure Logic W. S. Jevons
  19. Opuscules et fragments inedits G. W. Leibniz;L. Coutrat(ed.)
  20. Arithmetical principia, novo modo exposita G. Peano
  21. Amer. J. Math v.3 On the algebra of logic C. S. Peirce
  22. Vorlesungen iiber die Algebra der Logik v.3 E. Schroder
  23. Historia Math. v.10 no.1 순서와 위상구조의 관계 홍성사;홍영희
  24. Historia Math. v.12 no.1 유니버설대수학의 역사 홍영희