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Table des matières de ce fascicule | Article précédent | Article suivant
Larson, Suzanne
SV and related $f$-rings and spaces. Annales de la faculté des sciences de Toulouse Mathématiques, Sér. 6, 19 no. S1 (2010), p. 111-141
Analyses MR 2675724 | Zbl pre05799084
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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.
[A] Ali Rezaei Aliabad, Ahvaz. Pasting topological spaces at one point. Czech. Math. J. 2006, 56 (131), 1193 - 1206. MR 2280803 | Zbl 1164.54338
[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. MR 2382213 | Zbl 1149.46042
[BKW] Bigard, A.; Keimel, K.; Wolfenstein, S. Groupes et Anneaux Réticulés, Lecture Notes in Mathematics 608; Springer-Verlag: New York, 1977. MR 552653 | Zbl 0384.06022
[CD] Cherlin, G.; Dickmann, M. Real-closed rings I. Fund. Math. 1986, 126, 147-183. MR 843243 | Zbl 0605.54014
[D] Darnel, Michael. Theory of Lattice-Ordered Groups; Marcel Dekker, Inc: New York, 1995. MR 1304052 | Zbl 0810.06016
[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. MR 586984 | Zbl 0462.54009
[GJ] Gillman, L.; Jerison, M. Rings of Continuous Functions; D. Van Nostrand Publishing: New York, 1960. MR 116199 | Zbl 0093.30001
[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. MR 1247304 | Zbl 0799.06031
[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. MR 1239640 | Zbl 0817.06014
[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. MR 1173255 | Zbl 0801.54014
[HW2] Henriksen, M.; Wilson, R. Almost discrete SV-spaces. Topology and Applications 1992, 46, 89-97. MR 1184107 | Zbl 0791.54049
[K] Kuratowski, K. Topology, vol. 1; Academic Press; New York, 1966. MR 217751 | Zbl 0158.40802
[L1] Larson, S. Convexity conditions on $f$-rings. Canad. J. Math. 1986, 38, 48-64. MR 835035 | Zbl 0588.06011
[L2] Larson, S. $f$-Rings in which every maximal ideal contains finitely many minimal prime ideals. Comm. in Algebra 1997, 25 (12), 3859-3888. MR 1481572 | Zbl 0952.06026
[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. MR 1976272 | Zbl 1024.54015
[L4] Larson, S. Rings of continuous functions on spaces of finite rank and the SV property. Comm. in Algebra 2007, 35 (8), 2611 - 2627. MR 2345805 | Zbl 1146.54008
[L5] Larson, S. Images and open subspaces of SV spaces. Comm. in Algebra, 2008, 36, 1 - 13. MR 2387527 | Zbl 1147.54008
[L6] Larson, S. Functions that map cozerosets to cozerosets. Commentationes Mathematicae Universitatis Carolinae 2007, 48 (3), 507-521.
Article | MR 2374130 | Zbl pre05595996
[MW] Martinez, J; Woodward, S. Bezout and Prüfer $f$-Rings. Comm. in Algebra 1992, 20, 2975 - 2989. MR 1179272 | Zbl 0766.06018
[S1] Schwartz, N. The Basic Theory of Real Closed Spaces, AMS Memoirs 397; Amer. Math. Soc.: Providence, RI, 1989. MR 953224 | Zbl 0697.14015
[S2] Schwartz, N. Rings of continuous functions as real closed rings. Ordered Algebraic Structures (Curaçao 1995), Kluwer Acad. Publishing: Dordrecht, 1997, 277-313. MR 1445117 | Zbl 0885.46024
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