Fuchs, L. Arbitrarily large indecomposable divisible torsion modules over certain valuation domains. (English) Zbl 0611.13010 Rend. Semin. Mat. Univ. Padova 76, 247-254 (1986). In this paper, the author studies the existence of large indecomposable torsion modules: it is shown that there exist valuation domains R such that there are arbitrarily large torsion divisible R-modules. Reviewer: S.Raianu Cited in 1 ReviewCited in 11 Documents MSC: 13C12 Torsion modules and ideals in commutative rings Keywords:large indecomposable torsion modules; valuation domains PDF BibTeX XML Cite \textit{L. Fuchs}, Rend. Semin. Mat. Univ. Padova 76, 247--254 (1986; Zbl 0611.13010) Full Text: Numdam EuDML OpenURL References: [1] A.L.S. Corner , Fully rigid systems of modules . Numdam | Zbl 0712.16007 · Zbl 0712.16007 [2] B. Franzen - R. Göbel , The Brenner-Butler-Corner theorem and its application to modules (to appear in Abelian Group Theory, Proceedings Oberwolfach, 1985 ). MR 1011314 | Zbl 0667.20045 · Zbl 0667.20045 [3] L. Fuchs , On divisible modules over domains, Abelian Groups and Modules , Proc. of the Udine Conference, Springer-Verlag ( Wien - New York , 1985 ), pp. 341 - 356 . MR 789830 | Zbl 0574.13001 · Zbl 0574.13001 [4] L. Fuchs , On polyserial modules over valuation domains (to appear). MR 902514 | Zbl 0628.13013 · Zbl 0628.13013 [5] L. Fuchs - L. Salce , Modules over valuation domains , Lecture Notes in Pure and Applied Math. , vol. 97 , Marcel Dekker , 1985 . MR 786121 | Zbl 0578.13004 · Zbl 0578.13004 [6] E. Matlis , Cotorsion modules, Memoirs of Amer. Math. Soc. , 49 ( 1964 ). MR 178025 | Zbl 0135.07801 · Zbl 0135.07801 [7] S. Shelah , Infinite abelian groups, Whitehead problem and some constructions , Israel J. Math. , 18 ( 1974 ), pp. 243 - 256 . MR 357114 | Zbl 0318.02053 · Zbl 0318.02053 [8] C.P. Walker , Relative homological algebra and abelian groups , Illinois J. Math. , 40 ( 1966 ), pp. 186 - 209 . Article | MR 190210 | Zbl 0136.25601 · Zbl 0136.25601 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.