SV and related f -rings and spaces

Suzanne Larson[1]

  • [1] Loyola Marymount University Los Angeles, California 90045

Annales de la faculté des sciences de Toulouse Mathématiques (2010)

  • Volume: 19, Issue: S1, page 111-141
  • ISSN: 0240-2963

Abstract

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An f -ring A is an SV f -ring if for every minimal prime -ideal P of A , A / P is a valuation domain. A topological space X is an SV space if C ( X ) is an SV f -ring. SV f -rings and spaces were introduced in [HW1], [HW2]. Since then a number of articles on SV f -rings and spaces and on related f -rings and spaces have appeared. This article surveys what is known about these f -rings and spaces and introduces a number of new results that help to clarify the relationship between SV f -rings and spaces and related f -rings and spaces.

How to cite

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Larson, Suzanne. "SV and related $f$-rings and spaces." Annales de la faculté des sciences de Toulouse Mathématiques 19.S1 (2010): 111-141. <http://eudml.org/doc/115892>.

@article{Larson2010,
abstract = {An $f$-ring $A$ is an SV $f$-ring if for every minimal prime $\ell $-ideal $P$ of $A$, $A/P$ is a valuation domain. A topological space $X$ is an SV space if $C(X)$ is an SV $f$-ring. SV $f$-rings and spaces were introduced in [HW1], [HW2]. Since then a number of articles on SV $f$-rings and spaces and on related $f$-rings and spaces have appeared. This article surveys what is known about these $f$-rings and spaces and introduces a number of new results that help to clarify the relationship between SV $f$-rings and spaces and related $f$-rings and spaces.},
affiliation = {Loyola Marymount University Los Angeles, California 90045},
author = {Larson, Suzanne},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {-rings; SV-rings; partially ordered rings},
language = {eng},
month = {4},
number = {S1},
pages = {111-141},
publisher = {Université Paul Sabatier, Toulouse},
title = {SV and related $f$-rings and spaces},
url = {http://eudml.org/doc/115892},
volume = {19},
year = {2010},
}

TY - JOUR
AU - Larson, Suzanne
TI - SV and related $f$-rings and spaces
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2010/4//
PB - Université Paul Sabatier, Toulouse
VL - 19
IS - S1
SP - 111
EP - 141
AB - An $f$-ring $A$ is an SV $f$-ring if for every minimal prime $\ell $-ideal $P$ of $A$, $A/P$ is a valuation domain. A topological space $X$ is an SV space if $C(X)$ is an SV $f$-ring. SV $f$-rings and spaces were introduced in [HW1], [HW2]. Since then a number of articles on SV $f$-rings and spaces and on related $f$-rings and spaces have appeared. This article surveys what is known about these $f$-rings and spaces and introduces a number of new results that help to clarify the relationship between SV $f$-rings and spaces and related $f$-rings and spaces.
LA - eng
KW - -rings; SV-rings; partially ordered rings
UR - http://eudml.org/doc/115892
ER -

References

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