# $SV$-Rings and $SV$-Porings

• [1] Fakultät für Informatik und Mathematik, Universität Passau, Postfach 2540, 94030 Passau, Germany
• Volume: 19, Issue: S1, page 159-202
• ISSN: 0240-2963

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## Abstract

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$SV$-rings are commutative rings whose factor rings modulo prime ideals are valuation rings. $SV$-rings occur most naturally in connection with partially ordered rings (= porings) and have been studied only in this context so far. The present note first develops the theory of $SV$-rings systematically, without assuming the presence of a partial order. Particular attention is paid to the question of axiomatizability (in the sense of model theory). Partially ordered $SV$-rings ($SV$-porings) are introduced, and some elementary properties are exhibited. Finally, $SV$-rings are used to study convex subrings and convex extensions of porings, in particular of real closed rings.

## How to cite

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Schwartz, Niels. "$SV$-Rings and $SV$-Porings." Annales de la faculté des sciences de Toulouse Mathématiques 19.S1 (2010): 159-202. <http://eudml.org/doc/115895>.

@article{Schwartz2010,
abstract = {$SV$-rings are commutative rings whose factor rings modulo prime ideals are valuation rings. $SV$-rings occur most naturally in connection with partially ordered rings (= porings) and have been studied only in this context so far. The present note first develops the theory of $SV$-rings systematically, without assuming the presence of a partial order. Particular attention is paid to the question of axiomatizability (in the sense of model theory). Partially ordered $SV$-rings ($SV$-porings) are introduced, and some elementary properties are exhibited. Finally, $SV$-rings are used to study convex subrings and convex extensions of porings, in particular of real closed rings.},
affiliation = {Fakultät für Informatik und Mathematik, Universität Passau, Postfach 2540, 94030 Passau, Germany},
author = {Schwartz, Niels},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {SV-rings; axiomatizability; convex subrings; real closed rings; partially ordered rings},
language = {eng},
month = {4},
number = {S1},
pages = {159-202},
publisher = {Université Paul Sabatier, Toulouse},
title = {$SV$-Rings and $SV$-Porings},
url = {http://eudml.org/doc/115895},
volume = {19},
year = {2010},
}

TY - JOUR
AU - Schwartz, Niels
TI - $SV$-Rings and $SV$-Porings
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2010/4//
PB - Université Paul Sabatier, Toulouse
VL - 19
IS - S1
SP - 159
EP - 202
AB - $SV$-rings are commutative rings whose factor rings modulo prime ideals are valuation rings. $SV$-rings occur most naturally in connection with partially ordered rings (= porings) and have been studied only in this context so far. The present note first develops the theory of $SV$-rings systematically, without assuming the presence of a partial order. Particular attention is paid to the question of axiomatizability (in the sense of model theory). Partially ordered $SV$-rings ($SV$-porings) are introduced, and some elementary properties are exhibited. Finally, $SV$-rings are used to study convex subrings and convex extensions of porings, in particular of real closed rings.
LA - eng
KW - SV-rings; axiomatizability; convex subrings; real closed rings; partially ordered rings
UR - http://eudml.org/doc/115895
ER -

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