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Rings over which all modules are I 0-modules

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Abstract

Let A be a ring that does not contain an infinite set of idempotents that are orthogonal modulo the ideal SI(A A ). It is proved that all A-modules are I 0-modules if and only if either A is a right semi-Artinian, right V-ring or A/SI(A A ) is an Artinian serial ring and the square of the Jacobson radical of A/SI(A A ) isequal to zero.

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Authors and Affiliations

  1. Russian University of Trade and Ecomomics,  ,  

    A. A. Tuganbaev

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  1. A. A. Tuganbaev
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Correspondence to A. A. Tuganbaev.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 5, pp. 193–200, 2007.

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Tuganbaev, A.A. Rings over which all modules are I 0-modules. J Math Sci 156, 336–341 (2009). https://doi.org/10.1007/s10958-008-9270-5

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  • DOI: https://doi.org/10.1007/s10958-008-9270-5

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