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Hopficity and duo rings

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Abstract

The aim of this paper is to study the Hopfian property in the context of chain and duo rings. For such rings, we characterize Hopfian free modules and show that a direct sum of cyclic R-modules is Hopfian if and only if the sum is finite. This allows us to show that finitely generated modules over a local right duo ring, which has the FGC-property, are Hopfian and cancel in direct sums. Moreover, being finitely, hopficity, and the cancellation property are equivalent for modules over Artinian rings.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Auburn University, Auburn, AL, 36849, USA

    Ulrich Albrecht

  2. Department of Mathematics, Kennesaw State University, Kennesaw, GA, 30144, USA

    Francisco Javier Santillán-Covarrubias

Authors
  1. Ulrich Albrecht
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  2. Francisco Javier Santillán-Covarrubias
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Corresponding author

Correspondence to Ulrich Albrecht.

Additional information

Communicated by Gadadhar Misra.

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Albrecht, U., Santillán-Covarrubias, F.J. Hopficity and duo rings. Indian J Pure Appl Math 52, 369–374 (2021). https://doi.org/10.1007/s13226-021-00144-2

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  • DOI: https://doi.org/10.1007/s13226-021-00144-2

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