Kaplansky, Irving Modules over Dedekind rings and valuation rings. (English) Zbl 0046.25701 Trans. Am. Math. Soc. 72, 327-340 (1952). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 139 Documents MathOverflow Questions: Inverse of the Structure Theorem for Finitely Generated Modules over PID Keywords:rings, modules, fields PDFBibTeX XMLCite \textit{I. Kaplansky}, Trans. Am. Math. Soc. 72, 327--340 (1952; Zbl 0046.25701) Full Text: DOI References: [1] Reinhold Baer, Abelian groups without elements of finite order, Duke Math. J. 3 (1937), no. 1, 68 – 122. · Zbl 0016.20303 [2] Reinhold Baer, Abelian groups that are direct summands of every containing abelian group, Bull. Amer. Math. Soc. 46 (1940), 800 – 806. · Zbl 0024.14902 [3] Jean Braconnier, Sur les groupes topologiques localement compacts, J. Math. Pures Appl. (9) 27 (1948), 1 – 85 (French). · Zbl 0034.16401 [4] C. Chevalley, L’arithmétique dans les algèbres de matrices, Actualités Scientifiques et Industrielles, no. 323, Paris, 1936. · JFM 62.0102.01 [5] Irving Kaplansky, Maximal fields with valuations, Duke Math. J. 9 (1942), 303 – 321. · Zbl 0063.03135 [6] Irving Kaplansky, Elementary divisors and modules, Trans. Amer. Math. Soc. 66 (1949), 464 – 491. · Zbl 0036.01903 [7] L. Kulikoff, Zur Theorie der Abelschen Gruppen von beliebiger Mächtigkeit, Rec. Math. [Mat. Sbornik] N.S. 9 (51) (1941), 165 – 181 (Russian, with German summary). · JFM 67.0070.02 [8] L. Koulikoff, On the theory of Abelian groups of arbitrary power, Rec. Math. [Mat. Sbornik] N.S. 16 (58) (1945), 129 – 162 (Russian, with English summary). · Zbl 0061.03410 [9] W. Krull, Allgemeine Bewertungstheorie, Journal für Mathematik vol. 167 (1932) pp. 160-196. · JFM 58.0148.02 [10] Heinz Prüfer, Untersuchungen über die Zerlegbarkeit der abzählbaren primären Abelschen Gruppen, Math. Z. 17 (1923), no. 1, 35 – 61 (German). · JFM 49.0084.03 [11] Heinz Prüfer, Theorie der Abelschen Gruppen, Math. Z. 22 (1925), no. 1, 222 – 249 (German). · JFM 51.0115.01 [12] O. F. G. Schilling, The Theory of Valuations, Mathematical Surveys, No. 4, American Mathematical Society, New York, N. Y., 1950. · Zbl 0037.30702 [13] E. Steinitz, Rechtickige Systeme und Moduln in algebraischen Zahlkörpern, Math. Ann. vol. 71 (1912) pp. 328-354. · JFM 42.0230.02 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.