Geodesic
WEAK ISOMETRIES IN PARTIALLY ORDERED GROUPS
Acta mathematica Universitatis Comenianae, Tome 63 (1994) no. 2 
M. Jasem. WEAK ISOMETRIES IN PARTIALLY ORDERED GROUPS. Acta mathematica Universitatis Comenianae, Tome 63 (1994) no. 2. http://geodesic.mathdoc.fr/item/AMUC_1994_63_2_a8/
@article{AMUC_1994_63_2_a8,
     author = {M. Jasem},
     title = {WEAK {ISOMETRIES} {IN} {PARTIALLY} {ORDERED} {GROUPS}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {1994},
     volume = {63},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_1994_63_2_a8/}
}
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JO  - Acta mathematica Universitatis Comenianae
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ID  - AMUC_1994_63_2_a8
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%J Acta mathematica Universitatis Comenianae
%D 1994
%V 63
%N 2
%U http://geodesic.mathdoc.fr/item/AMUC_1994_63_2_a8/
%F AMUC_1994_63_2_a8

Voir la notice de l'article provenant de la source Comenius University

In this paper the author gives necessary and sufficient conditions under which to a stable weak isometry $f$ in a directed group $G$ there exists a direct decomposition $G=A\times B$ of $G$ such that $f(x)=x(A)-x(B)$ for each $x\in G$. Further, some results on weak isometries in partially ordered groups are established.