Geodesic
Some notes on the composite $G$-valuations
Archivum mathematicum, Tome 30 (1994) no. 4, pp. 271-275.

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In analogy with the notion of the composite semi-valuations, we define the composite $G$-valuation $v$ from two other $G$-valuations $w$ and $u$. We consider a lexicographically exact sequence $(a,\beta ):A_u\rightarrow B_v\rightarrow C_w$ and the composite $G$-valuation $v$ of a field $K$ with value group $B_v$. If the assigned to $v$ set $R_v=\lbrace x\in K/v(x)\ge 0$ or $v(x)$ non comparable to $0\rbrace $ is a local ring, then a $G$-valuation $w$ of $K$ into $C_w$ is defined with its assigned set $R_w$ a local ring, as well as another $G$-valuation $u$ of a residue field is defined with $G$-value group $A_u$.
Classification : 13A18
Keywords: composite semi-valuation; ordered group; G-homomorphism of ordered groups 
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     author = {Kontolatou, Angeliki},
     title = {Some notes on the composite $G$-valuations},
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     pages = {271--275},
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Kontolatou, Angeliki. Some notes on the composite $G$-valuations. Archivum mathematicum, Tome 30 (1994) no. 4, pp. 271-275. http://geodesic.mathdoc.fr/item/ARM_1994__30_4_a3/