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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Exterior powers and torsion free modules over discrete valuation rings


Author: David M. Arnold
Journal: Trans. Amer. Math. Soc. 170 (1972), 471-481
MSC: Primary 13C10
DOI: https://doi.org/10.1090/S0002-9947-1972-0304367-1
MathSciNet review: 0304367
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Abstract: Pure $ R$-submodules of the $ p$-adic completion of a discrete valuation ring $ R$ with unique prime ideal $ (p)$ (called purely indecomposable $ R$-modules) have been studied in detail. This paper contains an investigation of a new class of torsion free $ R$-modules of finite rank (called totally indecomposable $ R$-modules) properly containing the class of purely indecomposable $ R$-modules of finite rank. Exterior powers are used to construct examples of totally indecomposable modules.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0304367-1
Keywords: Torsion free modules, finite rank, discrete valuation ring, purely indecomposable, local endomorphism ring
Article copyright: © Copyright 1972 American Mathematical Society