Geodesic
Applications of Duality in the Theory of Finitely Generated Lattice-Ordered Abelian Groups
Canadian journal of mathematics, Tome 29 (1977) no. 2, pp. 243-254

Voir la notice de l'article provenant de la source Cambridge University Press

In a previous paper by the author [3], duality theorems for finitely generated vector lattices and lattice-ordered Abelian groups are described. In particular, the category of finitely generated semi-simple vector lattices is shown to be equivalent to a geometrical category V whose objects are topologically closed cones in Euclidean space, and whose morphisms, called ll-maps\ form a special subclass of the class of piece wise homogeneous linear maps between such cones. Under this categorical duality, finitely generated projective vector lattices and closed polyhedral cones correspond; indeed, the category of finitely generated projective vector lattices is equivalent to the dual of a category whose objects are Euclidean closed polyhedral cones and whose morphisms consist of all piecewise homogeneous linear maps between such cones. 
Beynon, W. M. Applications of Duality in the Theory of Finitely Generated Lattice-Ordered Abelian Groups. Canadian journal of mathematics, Tome 29 (1977) no. 2, pp. 243-254. doi: 10.4153/CJM-1977-026-4
@article{10_4153_CJM_1977_026_4,
     author = {Beynon, W. M.},
     title = {Applications of {Duality} in the {Theory} of {Finitely} {Generated} {Lattice-Ordered} {Abelian} {Groups}},
     journal = {Canadian journal of mathematics},
     pages = {243--254},
     year = {1977},
     volume = {29},
     number = {2},
     doi = {10.4153/CJM-1977-026-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-026-4/}
}
TY  - JOUR
AU  - Beynon, W. M.
TI  - Applications of Duality in the Theory of Finitely Generated Lattice-Ordered Abelian Groups
JO  - Canadian journal of mathematics
PY  - 1977
SP  - 243
EP  - 254
VL  - 29
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-026-4/
DO  - 10.4153/CJM-1977-026-4
ID  - 10_4153_CJM_1977_026_4
ER  - 
%0 Journal Article
%A Beynon, W. M.
%T Applications of Duality in the Theory of Finitely Generated Lattice-Ordered Abelian Groups
%J Canadian journal of mathematics
%D 1977
%P 243-254
%V 29
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-026-4/
%R 10.4153/CJM-1977-026-4
%F 10_4153_CJM_1977_026_4

[1] 1. Baker, K. A., Free vector lattices, Can. J. Math. 20 (1968), 58–66. Google Scholar

[2] 2. Beynon, W. M., Combinatorial aspects of piecewise linear maps, J. London Math. Soc. (2) (1974), 719–727. Google Scholar

[3] 3. Beynon, W. M. Duality theorems for finitely generated vector lattices, Proc. London Math. Soc. (3) 31 (1975), 114–128. Google Scholar

[4] 4. Beynon, W. M. On rational subdivisions of polyhedra with rational vertices, Can. J. Math. 29 (1977), 238–242. Google Scholar

[5] 5. Birkhoff, G. A., Lattice theory, A. M. S. Colloquium Publications Vol. XXV 3rd edition (1967). Google Scholar

[6] 6. Bleier, R. J., Archimedean vector lattices generated by 2 elements, Proc. Amer. Math. Soc. 39 (1973), 1–9. Google Scholar

[7] 7. Glaser, L. C., Geometrical combinatorial topology, Vol. 1, Van Nostrand Reinhold Mathematical Studies 27. Google Scholar

[8] 8. Rourke, C. P. and Sanderson, B. J., Introduction to piecewise-linear topology, Ergebnisse der Mathematik und ihrer Grenzgebiete Band 69 (Springer-Verlag, 1972). Google Scholar

[9] 9. Stallings, J. R., Lectures on polyhedral topology, Tata Institute of Fundamental Research, Bombay (1968). Google Scholar

Cité par Sources :