Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Settling a number of questions about hyper-Archimedean lattice-ordered groups


Authors: Paul Conrad and Jorge Martinez
Journal: Proc. Amer. Math. Soc. 109 (1990), 291-296
MSC: Primary 06F15
DOI: https://doi.org/10.1090/S0002-9939-1990-0998733-5
MathSciNet review: 998733
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This note contains the answers to several long-standing questions about hyper-Archimedean lattice-ordered groups. In particular, we construct such a lattice-ordered group which admits no embedding into an Archimedean lattice-ordered group with a strong order unit.


References [Enhancements On Off] (What's this?)

  • [AF] M. Anderson and T. Feil, Lattice-ordered groups, Reidel, Dordreacht, 1988. MR 937703 (90b:06001)
  • [Ba] K. A. Baker, Topological methods in the algebraic theory of vector lattices, Thesis, Harvard University, 1966.
  • [Be] S. J. Bernau, On hyper-archimedean vector lattices, Proc. Kon. Nederl. Akad. v. Wetensch. 77 (1974), 40-43. MR 0341017 (49:5767)
  • [BKW] A. Bigard, K. Keimel and S. Wolfenstein, Groupes et anneaux réticulés, Lecture Notes in Math., vol. 608, Springer, Berlin, 1977. MR 0552653 (58:27688)
  • [B$ _{1}$] R. Bleier, Minimal vector lattices, Bull. Austral. Math. Soc. 5 (1971), 411-413. MR 0295989 (45:5050)
  • [C$ _{1}$] P. Conrad, Some structure theorems for lattice-ordered groups, Trans. Amer. Math. Soc. 99 (1961), 212-240. MR 0121405 (22:12143)
  • [C$ _{2}$] -, Minimal vector lattices, Bull. Austral. Math. Soc. 4 (1971), 35-39. MR 0272692 (42:7573)
  • [C$ _{3}$] -, Epi-archimedean groups, Czeachoslovak Math. J. 24 (99) (1974), 192-218. MR 0347701 (50:203)
  • [CD] P. Conrad and M. Darnel, $ \ell $-groups with unique addition, Proc. First Symp. Ordered Algebraic Structures, Helderman, Berlin, 1986, pp. 15-27. MR 891445 (88i:06024)
  • [CHH] P. Conrad, J. Harvey, and W. C. Holland, The Hahn embedding theorem for lattice-ordered groups, Trans. Amer. Math. Soc. 108 (1963), 143-169. MR 0151534 (27:1519)
  • [CM] P. Conrad and J. Martinez, Signatures and discrete lattice-ordered groups, Alg. Universalis (to appear).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06F15

Retrieve articles in all journals with MSC: 06F15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-0998733-5
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society