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Free modules over hjelmslev rings in which not every maximal linearly independent subset is a basis

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Abstract

First it will be shown that every left-noetherian AH-ring is left-artinian. For an AH-ring R every finite linearly independent subset of a free left R-module V can be completed to a basis of V. But a maximal linearly independent subset of a free left R-module V need not be a basis of V. For an H-ring R, every maximal linearly independent subset of a free left R-module V is a basis of V if and only if the H-ring R is left-noetherian or V is finitely generated.

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  1. Mathematisches Institut, Technische Universität München, Arcisstr. 21, D-8000, München 2

    Alexander Kreuzer

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  1. Alexander Kreuzer
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Kreuzer, A. Free modules over hjelmslev rings in which not every maximal linearly independent subset is a basis. J Geom 45, 105–113 (1992). https://doi.org/10.1007/BF01225769

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  • DOI: https://doi.org/10.1007/BF01225769

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