IJPAM: Volume 80, No. 2 (2012)

TOPOLOGY AND VALUATION RINGS GENERATED ON
A SKEW FIELD BY A $G$-VALUATION

Angeliki Kontolatou$^1$, John Stabakis$^2$
$^{1,2}$Department of Mathematics
University of Patras
Patras, 26504, GREECE


Abstract. The basic idea in this paper is the existence of torsion in the value group of a generalized valuation defined on a skew field and named $G$-valuation. The existence of torsion causes a chaos in several parts of the whole theory and our attempt is to handle this disorder. It is interesting that the construction of the $G$-value group is based on the completion of a partially ordered group on the Kurepa's completion, which differs a little from the MacNeille's completion to which is based a classical valuation, for instance a semi-valuation. Next we examine whether basic conclusions for the topology on a valuated field are in valid here. Finally we study the ``valuation rings" defined by a $G$-valuation

Received: July 9, 2012

AMS Subject Classification: 12E15, 13A18, 54H13, 06F20

Key Words and Phrases: valuation ring, value group, $G$-valuation, skew topological G-valuated field

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 80
Issue: 2