Geodesic
On Properties of Interpolation Groups
Matematičeskie zametki, Tome 93 (2013) no. 2, pp. 295-304.

Voir la notice de l'article provenant de la source Math-Net.Ru

Partially ordered groups satisfying the interpolation condition (and not necessarily directed) are considered. It is proved that an isomorphism theorem holds for these groups (this theorem fails to hold for partially ordered groups in the general case). A criterion for almost orthogonality of positive elements of interpolation groups is found. The location of a subgroup associated with a pair of almost orthogonal elements in the lattice of subgroups of an interpolation group is described.
Keywords: partially ordered group, lattice of subgroups, almost orthogonality, Riesz–Fuchs group, pseudolattice-ordered group.
Mots-clés : interpolation group 
@article{MZM_2013_93_2_a13,
     author = {E. E. Shirshova},
     title = {On {Properties} of {Interpolation} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {295--304},
     publisher = {mathdoc},
     volume = {93},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a13/}
}
TY  - JOUR
AU  - E. E. Shirshova
TI  - On Properties of Interpolation Groups
JO  - Matematičeskie zametki
PY  - 2013
SP  - 295
EP  - 304
VL  - 93
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a13/
LA  - ru
ID  - MZM_2013_93_2_a13
ER  - 
%0 Journal Article
%A E. E. Shirshova
%T On Properties of Interpolation Groups
%J Matematičeskie zametki
%D 2013
%P 295-304
%V 93
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a13/
%G ru
%F MZM_2013_93_2_a13
E. E. Shirshova. On Properties of Interpolation Groups. Matematičeskie zametki, Tome 93 (2013) no. 2, pp. 295-304. http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a13/

[1] L. Fuks, Chastichno uporyadochennye algebraicheskie sistemy, Mir, M., 1965 | MR | Zbl

[2] V. M. Kopytov, Reshetochno uporyadochennye gruppy, Sovremennaya algebra, Nauka, M., 1984 | MR | Zbl

[3] E. E. Shirshova, “Gomomorfizmy, sokhranyayuschie $p$-ortogonalnost”, Fundament. i prikl. matem., 6:3 (2000), 939–952 | MR | Zbl

[4] L. Fuchs, “Riesz groups”, Ann. Scuola Norm. Sup. Pisa (3), 19 (1965), 1–34 | MR | Zbl

[5] E. E. Shirshova, “Svoistva gomomorfizmov grupp Rissa”, UMN, 46:5(281) (1991), 157–158 | MR | Zbl

[6] E. E. Shirshova, “Ob obobschenii ponyatiya ortogonalnosti i gruppakh Rissa”, Matem. zametki, 69:1 (2001), 122–132 | DOI | MR | Zbl

[7] E. E. Shirshova, “O gomomorfizmakh $pl$-grupp”, Fundament. i prikl. matem., 3:1 (1997), 303–314 | MR | Zbl

[8] P. Conrad, “Representation of partially ordered Abelian groups as groups of real valued functions”, Acta Math., 116 (1966), 199–221 | MR | Zbl

[9] A. M. W. Glass, “Polars and their application in directed interpolation groups”, Trans. Amer. Math. Soc., 166 (1972), 1–25 | DOI | MR | Zbl

[10] S. Leng, Algebra, Mir, M., 1968 | MR | Zbl

[11] M. Jakubíková, “Konvexe gerichtete Untergruppen der Rieszschen Gruppen”, Mat. Časopis Sloven. Akad. Vied, 21:1 (1971), 3–8 | MR | Zbl