Geodesic
Implications between Conditions on l-Groups
Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 1-6

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

The study of lattice-ordered groups (l-groups) in recent years has yielded several publications concerning the lattice of all convex l-subgroups (denoted by Γ(G)). As for example, in [3], Conrad has shown a direct connection between one possible structure of Γ(G) as a lattice and certain finite conditions on the elements of the group G. In the process of developing variations of this approach, there has been imposed several different conditions on G and Γ(G). For instance, it was proposed by Conrad that if all the minimal prime subgroups have non-zero polars, then the group elements would all be finite-valued. In this paper we show that in general this is not true. 
Pedersen, Franklin D. Implications between Conditions on l-Groups. Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 1-6. doi: 10.4153/CJM-1970-001-6
@article{10_4153_CJM_1970_001_6,
     author = {Pedersen, Franklin D.},
     title = {Implications between {Conditions} on {l-Groups}},
     journal = {Canadian journal of mathematics},
     pages = {1--6},
     year = {1970},
     volume = {22},
     number = {1},
     doi = {10.4153/CJM-1970-001-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1970-001-6/}
}
TY  - JOUR
AU  - Pedersen, Franklin D.
TI  - Implications between Conditions on l-Groups
JO  - Canadian journal of mathematics
PY  - 1970
SP  - 1
EP  - 6
VL  - 22
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1970-001-6/
DO  - 10.4153/CJM-1970-001-6
ID  - 10_4153_CJM_1970_001_6
ER  - 
%0 Journal Article
%A Pedersen, Franklin D.
%T Implications between Conditions on l-Groups
%J Canadian journal of mathematics
%D 1970
%P 1-6
%V 22
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1970-001-6/
%R 10.4153/CJM-1970-001-6
%F 10_4153_CJM_1970_001_6

[1] 1. Birkhoff, G., Lattice theory, rev. éd. Amer. Math. Soc. Colloq. Publ. Vol. 25 (Amer. Math. Soc, Providence, R.I., 1948). Google Scholar

[2] 2. Conrad, P. F., Some structure theorems for lattice-ordered groups, Trans. Amer. Math. Soc. 99 (1961), 212–240. Google Scholar

[3] 3. Conrad, P. F., The lattice of all convex l-subgroups of a lattice-ordered group, Czechoslovak Math. J. 15 (90) (1965), 101–123. Google Scholar

[4] 4. Conrad, P. F., Harvey, J., and Holland, C., The Hahn embedding theorem for abelian lattice-ordered groups, Trans. Amer. Math. Soc. 108 (1963), 143–169. Google Scholar

[5] 5. Pedersen, F., Contributions to the theory of regular subgroups and prime subgroups of a lattice ordered group, Doctoral Dissertation, Tulane University, New Orleans, Louisiana, 1967. Google Scholar

Cité par Sources :