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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
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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Keywords: Torsion free modules, finite rank, discrete valuation ring, purely indecomposable, local endomorphism ring
Article copyright: © Copyright 1972 American Mathematical Society