Abstract
We consider modules over integral domains, and investigate direct sums of finite rank torsion-free modules whose endomorphism rings are completely integrally closed elementary divisor domains. The main result (Theorem 4.4) is a Krull-Schmidt-Azumaya type theorem: if a module A is a direct sum of finite rank torsion-free modules each of which is quasi-isomorphic to a member of a semi-rigid system with the mentioned type of endomorphism ring, then every summand of A admits the same kind of direct decomposition. The uniqueness of such decompositions is established up to quasi-isomorphism (Theorem 4.5).
In memoriam Elbert Walker
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Fuchs, L. (2020). Elementary Divisor Domains as Endomorphism Rings. In: Nguyen, H., Kreinovich, V. (eds) Algebraic Techniques and Their Use in Describing and Processing Uncertainty. Studies in Computational Intelligence, vol 878. Springer, Cham. https://doi.org/10.1007/978-3-030-38565-1_3
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DOI: https://doi.org/10.1007/978-3-030-38565-1_3
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