Geodesic
SV and related f-rings and spaces
Larson, Suzanne1
1 Loyola Marymount University Los Angeles, California 90045
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Numéro spécial : Actes de la Conférence sur les anneaux ordonnés en honneur de Melvin Henriksen, Université d’état de Louisiane à Bâton Rouge, 2007, Tome 19 (2010) no. S1, pp. 111-141.

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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.

DOI : 10.5802/afst.1278

Larson, Suzanne 1

1 Loyola Marymount University Los Angeles, California 90045 
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Larson, Suzanne. SV and related $f$-rings and spaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Numéro spécial : Actes de la Conférence sur les anneaux ordonnés en honneur de Melvin Henriksen, Université d’état de Louisiane à Bâton Rouge, 2007, Tome 19 (2010) no. S1, pp. 111-141. doi : 10.5802/afst.1278. https://geodesic-test.mathdoc.fr/articles/10.5802/afst.1278/

[A] Ali Rezaei Aliabad, Ahvaz. Pasting topological spaces at one point. Czech. Math. J. 2006, 56 (131), 1193 - 1206. | Zbl | MR

[BH] Banerjee, B; Henriksen, M. Ways in which C(X) mod a prime ideal can be a valuation domain; something old and something new. Positivity (Trends in Mathematics), Birkhäuser Basel: Switzerland, 2007, 1- 25. | Zbl | MR

[BKW] Bigard, A.; Keimel, K.; Wolfenstein, S. Groupes et Anneaux Réticulés, Lecture Notes in Mathematics 608; Springer-Verlag: New York, 1977. | Zbl | MR

[CD] Cherlin, G.; Dickmann, M. Real-closed rings I. Fund. Math. 1986, 126, 147-183. | Zbl | MR

[D] Darnel, Michael. Theory of Lattice-Ordered Groups; Marcel Dekker, Inc: New York, 1995. | Zbl | MR

[DHH] Dashiell, F.; Hager, A.; Henriksen, M. Order-Cauchy completions of rings and vector lattices of continuous functions. Canad. J. Math. 1980, 32 (3), 657-685. | Zbl | MR

[GJ] Gillman, L.; Jerison, M. Rings of Continuous Functions; D. Van Nostrand Publishing: New York, 1960. | Zbl | MR

[HL] Henriksen, M.; Larson, S. Semiprime f-rings that are subdirect products of valuation domains. Ordered Algebraic Structures (Gainesville, FL 1991), Kluwer Acad. Publishing: Dordrecht, 1993, 159-168. | Zbl | MR

[HLMW] Henriksen, M.; Larson, S.; Martinez, J.; Woods, R. G. Lattice-ordered algebras that are subdirect products of valuation domains. Trans. Amer. Math. Soc. 1994, 345, 193-221. | Zbl | MR

[HW1] Henriksen, M.; Wilson, R. When is C(X)/P a valuation ring for every prime ideal P? Topology and Applications 1992, 44, 175-180. | Zbl | MR

[HW2] Henriksen, M.; Wilson, R. Almost discrete SV-spaces. Topology and Applications 1992, 46, 89-97. | Zbl | MR

[K] Kuratowski, K. Topology, vol. 1; Academic Press; New York, 1966. | Zbl | MR

[L1] Larson, S. Convexity conditions on f-rings. Canad. J. Math. 1986, 38, 48-64. | Zbl | MR

[L2] Larson, S. f-Rings in which every maximal ideal contains finitely many minimal prime ideals. Comm. in Algebra 1997, 25 (12), 3859-3888. | Zbl | MR

[L3] Larson, S. Constructing rings of continuous functions in which there are many maximal ideals with nontrivial rank. Comm. in Algebra 2003, 31 (5), 2183-2206. | Zbl | MR

[L4] Larson, S. Rings of continuous functions on spaces of finite rank and the SV property. Comm. in Algebra 2007, 35 (8), 2611 - 2627. | Zbl | MR

[L5] Larson, S. Images and open subspaces of SV spaces. Comm. in Algebra, 2008, 36, 1 - 13. | Zbl | MR

[L6] Larson, S. Functions that map cozerosets to cozerosets. Commentationes Mathematicae Universitatis Carolinae 2007, 48 (3), 507-521. | MR

[MW] Martinez, J; Woodward, S. Bezout and Prüfer f-Rings. Comm. in Algebra 1992, 20, 2975 - 2989. | Zbl | MR

[S1] Schwartz, N. The Basic Theory of Real Closed Spaces, AMS Memoirs 397; Amer. Math. Soc.: Providence, RI, 1989. | Zbl | MR

[S2] Schwartz, N. Rings of continuous functions as real closed rings. Ordered Algebraic Structures (Curaçao 1995), Kluwer Acad. Publishing: Dordrecht, 1997, 277-313. | Zbl | MR

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