SV and related $f$-rings and spaces

Suzanne Larson

doi:10.5802/afst.1278

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, Serie 6, Volume 19 (2010) no. S1, pp. 111-141.

Abstract
Abstract

An $f$ -ring $A$ is an SV $f$ -ring if for every minimal prime $ℓ$ -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.

MR

DOI: 10.5802/afst.1278

Author's affiliations:

Suzanne Larson ¹

¹ Loyola Marymount University Los Angeles, California 90045

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     title = {SV and related $f$-rings and spaces},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {111--141},
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Suzanne Larson. SV and related $f$-rings and spaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 19 (2010) no. S1, pp. 111-141. doi : 10.5802/afst.1278. https://afst.centre-mersenne.org/articles/10.5802/afst.1278/

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