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The Structure of Modules over Hereditary Rings

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Abstract

Let A be a bounded hereditary Noetherian prime ring. For an A-module M A , we prove that M is a finitely generated projective \({A \mathord{\left/ {\vphantom {A {r\left( M \right)}}} \right. \kern-\nulldelimiterspace} {r\left( M \right)}}\)-module if and only if M is a \({\pi }\)-projective finite-dimensional module, and either M is a reduced module or A is a simple Artinian ring. The structure of torsion or mixed \({\pi }\)-projective A-modules is completely described.

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Authors and Affiliations

  1. Moscow Power Engineering Institute, Russia

    A. A. Tuganbaev

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  1. A. A. Tuganbaev
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Tuganbaev, A.A. The Structure of Modules over Hereditary Rings. Mathematical Notes 68, 627–639 (2000). https://doi.org/10.1023/A:1026675709016

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  • DOI: https://doi.org/10.1023/A:1026675709016

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