On a conjecture regarding nonstandard uniserial modules
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- by Paul C. Eklof and Saharon Shelah PDF
- Trans. Amer. Math. Soc. 340 (1993), 337-351 Request permission
Abstract:
We consider the question of which valuation domains (of cardinality ${\aleph _1}$) have nonstandard uniserial modules. We show that a criterion conjectured by Osofsky is independent of ${\text {ZFC}} + {\text {GCH}}$.References
- Silvana Bazzoni, Laszlo Fuchs, and Luigi Salce, The hierarchy of uniserial modules over a valuation domain, Forum Math. 7 (1995), no. 2, 247–277. MR 1316949, DOI 10.1515/form.1995.7.247
- Silvana Bazzoni and Luigi Salce, On nonstandard uniserial modules over valuation domains and their quotients, J. Algebra 128 (1990), no. 2, 292–305. MR 1036392, DOI 10.1016/0021-8693(90)90024-I
- Silvana Bazzoni and Luigi Salce, Elongations of uniserial modules over valuation domains, J. Algebra 146 (1992), no. 2, 304–317. MR 1152907, DOI 10.1016/0021-8693(92)90070-3
- Silvana Bazzoni and Luigi Salce, Equimorphism classes of uniserial modules over valuation domains, Arch. Math. (Basel) 58 (1992), no. 1, 14–23. MR 1139381, DOI 10.1007/BF01198637
- Keith J. Devlin, Constructibility, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1984. MR 750828, DOI 10.1007/978-3-662-21723-8
- Keith J. Devlin and Saharon Shelah, A weak version of $\diamondsuit$ which follows from $2^{\aleph _{0}}<2^{\aleph _{1}}$, Israel J. Math. 29 (1978), no. 2-3, 239–247. MR 469756, DOI 10.1007/BF02762012
- Paul C. Eklof, A transfer theorem for nonstandard uniserials, Proc. Amer. Math. Soc. 114 (1992), no. 3, 593–600. MR 1074751, DOI 10.1090/S0002-9939-1992-1074751-8
- Paul C. Eklof and Alan H. Mekler, Almost free modules, North-Holland Mathematical Library, vol. 46, North-Holland Publishing Co., Amsterdam, 1990. Set-theoretic methods. MR 1055083
- Berthold Franzen and Rüdiger Göbel, Nonstandard uniserial modules over valuation domains, Results Math. 12 (1987), no. 1-2, 86–94. MR 911463, DOI 10.1007/BF03322380
- László Fuchs and Luigi Salce, Modules over valuation domains, Lecture Notes in Pure and Applied Mathematics, vol. 97, Marcel Dekker, Inc., New York, 1985. MR 786121
- László Fuchs and Saharon Shelah, Kaplansky’s problem on valuation rings, Proc. Amer. Math. Soc. 105 (1989), no. 1, 25–30. MR 929431, DOI 10.1090/S0002-9939-1989-0929431-3
- Barbara L. Osofsky, Constructing nonstandard uniserial modules over valuation domains, Azumaya algebras, actions, and modules (Bloomington, IN, 1990) Contemp. Math., vol. 124, Amer. Math. Soc., Providence, RI, 1992, pp. 151–164. MR 1144034, DOI 10.1090/conm/124/1144034
- Barbara L. Osofsky, A construction of nonstandard uniserial modules over valuation domains, Bull. Amer. Math. Soc. (N.S.) 25 (1991), no. 1, 89–97. MR 1085826, DOI 10.1090/S0273-0979-1991-16032-5
- Saharon Shelah, Nonstandard uniserial module over a uniserial domain exists, Around classification theory of models, Lecture Notes in Math., vol. 1182, Springer, Berlin, 1986, pp. 135–150. MR 850056, DOI 10.1007/BFb0098508
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 340 (1993), 337-351
- MSC: Primary 13C13; Secondary 03E35, 03E75, 13A18, 13L05
- DOI: https://doi.org/10.1090/S0002-9947-1993-1159192-2
- MathSciNet review: 1159192