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 $A_u$.
@article{107513,
author = {Angeliki Kontolatou},
title = {Some notes on the composite $G$-valuations},
journal = {Archivum Mathematicum},
volume = {030},
year = {1994},
pages = {271-275},
zbl = {0829.13002},
mrnumber = {1322571},
language = {en},
url = {http://dml.mathdoc.fr/item/107513}
}
Kontolatou, Angeliki. Some notes on the composite $G$-valuations. Archivum Mathematicum, Tome 030 (1994) pp. 271-275. http://gdmltest.u-ga.fr/item/107513/
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