Some notes on the composite G -valuations

Angeliki Kontolatou

Archivum Mathematicum (1994)

  • Volume: 030, Issue: 4, page 271-275
  • ISSN: 0044-8753

Abstract

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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 , β ) : A u → B v → 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 = { x ∈ K / v ( x ) ≥ 0 or v ( x ) non comparable to 0 } 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 .

How to cite

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Kontolatou, Angeliki. "Some notes on the composite $G$-valuations." Archivum Mathematicum 030.4 (1994): 271-275. <http://eudml.org/doc/247541>.

@article{Kontolatou1994,
abstract = {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 $A_u$.},
author = {Kontolatou, Angeliki},
journal = {Archivum Mathematicum},
keywords = {composite semi-valuation; ordered group; G-homomorphism of ordered groups; composite -valuation},
language = {eng},
number = {4},
pages = {271-275},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Some notes on the composite $G$-valuations},
url = {http://eudml.org/doc/247541},
volume = {030},
year = {1994},
}

TY - JOUR
AU - Kontolatou, Angeliki
TI - Some notes on the composite $G$-valuations
JO - Archivum Mathematicum
PY - 1994
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 030
IS - 4
SP - 271
EP - 275
AB - 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 $A_u$.
LA - eng
KW - composite semi-valuation; ordered group; G-homomorphism of ordered groups; composite -valuation
UR - http://eudml.org/doc/247541
ER -

References

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  1. Embedding groups into linear or lattice structures, Bull. Cal. Math. Soc. 82 (1987), 290-297. (1987) MR1134208
  2. Semi-valuations and groups of divisibility, Canad. Journ. of Math. 21 (1969), 576-591. (1969) Zbl0177.06501MR0242819
  3. Theorie des valuations, Les presses de l’ Universite de Montreal (1968). (1968) MR0249425

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