Geodesic
States on unital partially-ordered groups
Kybernetika, Tome 38 (2002) no. 3, p. [297].

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We study states on unital po-groups which are not necessarily commutative as normalized positive real-valued group homomorphisms. We show that in contrast to the commutative case, there are examples of unital po-groups having no state. We introduce the state interpolation property holding in any Abelian unital po-group, and we show that it holds in any normal-valued unital $\ell $-group. We present a connection among states and ideals of po-groups, and we describe extremal states on the state space of unital po-groups.
Classification : 06B10, 06F15
Keywords: non-commutative group; partially ordered groups 
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     author = {Dvure\v{c}enskij, Anatolij},
     title = {States on unital partially-ordered groups},
     journal = {Kybernetika},
     pages = {[297]},
     publisher = {mathdoc},
     volume = {38},
     number = {3},
     year = {2002},
     mrnumber = {1944311},
     zbl = {1265.06052},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2002__38_3_a6/}
}
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Dvurečenskij, Anatolij. States on unital partially-ordered groups. Kybernetika, Tome 38 (2002) no. 3, p. [297]. http://geodesic.mathdoc.fr/item/KYB_2002__38_3_a6/