Real Algebraic and Analytic Geometry |

Positivity and convexity in rings of fractions.

e-mail:

Submission: 2007, May 31.

*Abstract:
Given a commutative ring $A$ equipped with a preordering $A^+$ (in the most
general sense, see below), we look for a fractional ring extension (= ``ring
of quotients'' in the sense of Lambek et al. [L]) as big as possible such
that $A^+$ extends to a preordering $R^+$ of $R$ (i.e. with
$A \cap R^+ = A^+$) in a natural way. We then
ask for subextensions $A \subset B$ of $A \subset R$ such that $A$ is convex
in $B$ with respect to $B^+ := B \cap R^+$.*

Mathematics Subject Classification (2000): 13J25, 13J30, 13F05.

Keywords and Phrases: preordered ring extension, positively dense set, convexity cover, positivity divisor, convexity divisor.

**Full text**, 50p.:
dvi 214k,
ps.gz 245k,
pdf 349k.

Server Home Page